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Microwave Spectra and Molecular Structures of Organic Molecules and Hydrogen Bonded Dimers

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MICROWAVE SPECTRA AND MOLECULAR STRUCTURES OF ORGANIC
MOLECULES AND HYDROGEN BONDED DIMERS
by
Aaron Matthew Pejlovas
_____________________________
Copyright © Aaron Matthew Pejlovas 2018
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
WITH A MAJOR IN CHEMISTRY
In the Graduate College
THE UNIVERSITY OF ARIZONA
2018
ProQuest Number: 10748431
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THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
As members of the Dissertation Committee, we certify that we have read the
dissertation prepared by Aaron M. Pejlovas, titled Microwave Spectra and Molecular
Structures of Organic Molecules and Hydrogen Bonded Dimers and recommend that it
be accepted as fulfilling the dissertation requirement for the Degree of Doctor of
Philosophy.
p
Date: April 2,2018
Stephen G. Kukolich
Date: April 2,2018
Dr. Michael F. Brown
Date: April 2,2018
Dr. Dennis L. Lichtenberger
Date: April 2,2018
Final approval and acceptance of this dissertation is contingent upon the candidate's
submission of the final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and
recommend that it be accepted as fulfilling the dissertation requirement.
Date: Apral 2, 2018
ertation D ector: Dr. Stephen G. Kukolich
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of the requirements for
an advanced degree at the University of Arizona and is deposited in the University
Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission,
provided that an accurate acknowledgement of the source is made. Requests for
permission for extended quotation from or reproduction of this manuscript in whole or in
part may be granted by the head of the major department or the Dean of the Graduate
College when in his or her judgment the proposed use of the material is in the interests
of scholarship. In all other instances, however, permission must be obtained from the
author.
SIGNED: Aaron Matthew Pejlovas
3
ACKNOWLEDGEMENTS
I want to thank Dr. Stephen G. Kukolich for all his guidance throughout my
journey of graduate school. Without his advice and mentorship, I would not be the
scientist I have developed into today. I also want to acknowledge all of the professors I
have had, in my undergraduate career here at the University of Arizona as well as my
graduate career, teaching me the fundamentals of the wonderful field of chemistry.
Additionally, I want to acknowledge the University of Arizona for the great
education I received throughout my tenure here. It has been an honor to have been able
to complete my graduate degree at the same great university I attended for my
Bachelor’s. Lastly, I would like to thank the National Science Foundation for the funding
to perform the research presented in this dissertation. I look forward to my journey
ahead, wherever my career and life may take me.
4
DEDICATION
For my mom, dad, family, and beautiful loving wife, Rhianna. Thank you all for the
support and love that helped me get through this endeavor.
5
Table of Contents
LIST OF FIGURES ........................................................................................................ 11
LIST OF TABLES .......................................................................................................... 15
ABSTRACT ................................................................................................................... 23
1. INTRODUCTION ....................................................................................................... 24
2. RESEARCH METHODS ........................................................................................... 31
2.1 INTRODUCTION ................................................................................................. 31
2.2 MICROWAVE SPECTROMETER ........................................................................ 31
2.3 SAMPLE PREPARATION .................................................................................... 36
3. THEORY AND COMPUTATIONS ............................................................................. 38
3.1 THEORY .............................................................................................................. 38
3.1.1 SYMMETRIC TOP ENERGY LEVELS .......................................................... 38
3.1.2 ASYMMETRIC TOP ENERGY LEVELS ........................................................ 41
3.1.3 CENTRIFUGAL DISTORTION CORRECTIONS ........................................... 43
3.1.4 MICROWAVE SELECTION RULES .............................................................. 44
3.1.5 NUCLEAR SPIN ANGULAR MOMENTUM.................................................... 45
3.2 COMPUATIONAL METHODS ............................................................................. 47
3.3 LEAST SQUARES STRUCTURE FITTING ......................................................... 50
4. MICROWAVE MEASUREMENTS AND STRUCTURES OF LARGE ORGANIC
MOLECULES ................................................................................................................ 53
6
4.1 CYCLOPROPANECARBOXYLIC ACID............................................................... 54
4.1.1 INTRODUCTION ........................................................................................... 54
4.1.2 MICROWAVE MEASUREMENTS ................................................................. 55
4.1.3 CALCULATIONS ........................................................................................... 58
4.1.4 ROTATIONAL CONSTANTS ......................................................................... 60
4.1.5 MOLECULAR STRUCTURE ......................................................................... 61
4.1.6 DISCUSSION ................................................................................................ 62
4.2 1,2-CYCLOHEXANEDIONE ................................................................................ 66
4.2.1 INTRODUCTION ........................................................................................... 66
4.2.2 MICROWAVE MEASUREMENTS ................................................................. 67
4.2.3 CALCULATIONS ........................................................................................... 71
4.2.4 ROTATIONAL CONSTANTS ......................................................................... 72
4.2.5 MOLECULAR STRUCTURE ......................................................................... 73
4.2.6 DISCUSSION ................................................................................................ 75
5. MICROWAVE MEASUREMENTS ON MOLECULES WITH ELECTRIC
QUADRUPOLE INTERACTIONS.................................................................................. 77
5.1 MALEIMIDE ......................................................................................................... 78
5.1.1 INTRODUCTION ........................................................................................... 78
5.1.2 MICROWAVE MEASUREMENTS ................................................................. 79
5.1.3 CALCULATIONS ........................................................................................... 82
7
5.1.4 ROTATIONAL CONSTANTS ......................................................................... 83
5.1.5 MOLECULAR STRUCTURE ......................................................................... 84
5.1.6 DISCUSSION ................................................................................................ 87
5.2 PHTHALIMIDE ..................................................................................................... 89
5.2.1 INTRODUCTION ........................................................................................... 89
5.2.2 MICROWAVE MEASUREMENTS ................................................................. 90
5.2.3 CALCULATIONS ........................................................................................... 93
5.2.4 ROTATIONAL CONSTANTS ......................................................................... 93
5.2.5 MOLECULAR STRUCTURE ......................................................................... 96
5.2.6 DISCUSSION ................................................................................................ 99
5.3 4a,8a-AZABORANAPHTHALENE ..................................................................... 101
5.3.1 INTRODUCTION ......................................................................................... 101
5.3.2 CALCULATIONS ......................................................................................... 103
5.3.3 MICROWAVE MEASUREMENTS ............................................................... 105
5.3.4 ROTATIONAL AND QUADRUPOLE COUPLING CONSTANTS................. 111
5.3.5 GAS PHASE STRUCTURE ......................................................................... 114
5.3.6 DISCUSSION .............................................................................................. 119
6. MICROWAVE SPECTRA OF DOUBLY HYDROGEN BONDED DIMERS ............. 123
6.1 CYCLOPROPANECARBOXYLIC ACID – FORMIC ACID DIMER .................... 124
6.1.1 INTRODUCTION ......................................................................................... 124
8
6.1.2 MICROWAVE MEASUREMENTS ............................................................... 125
6.1.3 CALCULATIONS ......................................................................................... 130
6.1.4 ROTATIONAL CONSTANTS ....................................................................... 132
6.1.5 MOLECULAR STRUCTURE ....................................................................... 133
6.1.6 DISCUSSION .............................................................................................. 135
6.2 1,2-CYCLOHEXANEDIONE (MONOENOLIC) – FORMIC ACID DIMER........... 138
6.2.1 INTRODUCTION ......................................................................................... 138
6.2.2 MICROWAVE MEASUREMENTS ............................................................... 138
6.2.3 CALCULATIONS ......................................................................................... 143
6.2.4 ROTATIONAL CONSTANTS ....................................................................... 144
6.2.5 MOLECULAR STRUCTURE ....................................................................... 145
6.2.6 DISCUSSION .............................................................................................. 146
6.3 MALEIMIDE – FORMIC ACID DIMER ............................................................... 148
6.3.1 INTRODUCTION ......................................................................................... 148
6.3.2 CALCULATIONS, MICROWAVE MEASUREMENTS, AND DATA ANALYSIS
.............................................................................................................................. 149
6.3.3 CONCLUSIONS .......................................................................................... 157
6.4 TROPOLONE – FORMIC ACID DIMER ............................................................ 158
6.4.1 INTRODUCTION ......................................................................................... 158
6.4.2 MICROWAVE MEASUREMENTS ............................................................... 160
9
6.4.3 CALCULATIONS AND ROTATIONAL CONSTANTS .................................. 161
6.4.4 DISCUSSION .............................................................................................. 162
7. CONCLUDING REMARKS ..................................................................................... 165
8. APPENDIX A ........................................................................................................... 171
9. WORKS CITED ....................................................................................................... 189 10
LIST OF FIGURES
Figure 1.1
Ground state structure of cyclopropanecarboxylic acid. A higher energy
conformer was observed after a rotation of the carboxylic acid moiety about the C1-C9
bond................................................................................................................................27
Figure 1.2
Molecular structure of 1,2-cyclohexanedione in its monoenolic form, which
was readily observed under the gas phase experimental conditions. The dione form was
not observed in these studies.........................................................................................27
Figure 1.3
Molecular structures of A) maleimide, B) phthalimide, and C) 4a,8a-
azaboranaphthalene. These molecules all exhibit the electric quadrupole interactions
caused by the nuclear spin of 14N, 10B, and 11B..............................................................29
Figure 2.2.1 Block diagram of the electronics for the pulsed-beam Fourier transform
microwave spectrometer.................................................................................................32
Figure 2.2.2 Pulse sequence of spectrometer. The valve opens and after a 1 ms delay,
a short 1 μs pulse of microwave radiation is sent through the microwave switch and the
radiation fills the cavity. After a short time, the PICO scope is triggered and 100 μs of
data is collected..............................................................................................................34
Figure 2.2.3 Diagram showing directional coupler used to monitor reflected microwave
signal..............................................................................................................................35
Figure 2.3.1 Specialized glass sample cell used for the microwave experiments in this
dissertation, shown with two blue caps...........................................................................37
Figure 4.1.1 Structures of the two conformers of CPCA. The conformer shown on top
was lower energy than the conformer shown on the bottom. The difference in energies
11
of these two conformers was 373.1 cm-1 obtained from the B3LYP/aug-cc-pVQZ
calculation.......................................................................................................................57
Figure 4.1.2 Example transitions of the low energy conformer (left) and higher energy
conformer (right) taken of the 000 to 101 transition. Both transitions were recorded after
~230 pulsed-beam cycles...............................................................................................65
Figure 4.2.1 The best fit structure of 1,2-cyclohexanedione (enol tautomer) showing the
best fit A) bond lengths (Å) and B) the interbond angles (degrees) for the cyclohexane
ring. The C3-C5-C2 bond angle passes over the C5-H16 bond. All C-H bond lengths
are 1.09(1) Å...................................................................................................................67
Figure 5.1.1 Best fit structure of Maleimide showing the fit bond lengths (Å) and angles
(°). The bond lengths and angles are equivalent on the corresponding side across the
symmetry axis.................................................................................................................81
Figure 5.2.1 Best fit structure showing fit bond lengths (top, in Å) and angles (bottom,
in °). Also shown are the a and b principle axes within the molecule.............................92
Figure 5.3.1 Electron density mapped with the electrostatic potential (Iso Val = 0.0004)
of A) naphthalene and B) BN-naphthalene from the total SCF density using B3LYP/augcc-pVTZ. Red is the most electron rich and blue is electron deficient..........................104
Figure 5.3.2 Example transitions showing the hyperfine splitting from the 10B14N
(stimulation at 5643.680 MHz, 129 pulsed beam cycles), 11B13C4 or 13C12 (stimulation
at 3887.160 MHz, 2436 pulsed beam cycles), and 11B15N (stimulation at 5619.530 MHz,
7803 pulsed beam cycles) isotopologues.....................................................................109
Figure 5.3.3 Best fit structure showing bond lengths (Å) and angles (º). Only half of the
bond lengths and angles are shown in the cyclic ring structure due to the symmetry of
12
the molecule. All C-H bond lengths were held fixed to calculated equilibrium values and
so are not shown..........................................................................................................116
Figure 6.1.1 Example transitions of the parent isotopologue (6965.580 MHz
stimulation), the 13C isotopologue at the C16 position (6876.240 MHz stimulation), and
the 13C isotopologue at the equivalent positions of C3 and C6 (6878.020 MHz
stimulation) of the 404 – 505 transition (from left to right) taken at 300 pulsed-beam
cycles for each transition shown...................................................................................126
Figure 6.1.2 Calculated structures of the low energy (top) and higher energy (bottom)
CPCA-FA conformers using B97D with aug-cc-pVTZ basis. Also shown superimposed
on the low energy conformer are the a and b principle axes and the visualization of the
parameter φ (phi) used in the structure fit.....................................................................129
Figure 6.1.3 Plot showing the variation of the “best-fit” standard deviation for the
nonlinear least squares structure fit with the angle φ. The variation of the angle φ
represents the rotation of the FA moiety in the x-y Cartesian plane and changes the
relative lengths of the two hydrogen bonds..................................................................134
Figure 6.2.1 Best fit structure of the 1,2-CDO and FA hydrogen-bonded dimer.........139
Figure 6.2.2 Example of observed transition for 1,2-CDO – FA parent (505-606, 245
pulsed-beam cycles) at stimulating frequency 5860.900 MHz. The horizontal axis
represents the difference of the observed transition from the stimulating frequency,
shown in KHz................................................................................................................142
Figure 6.3.1 Best fit structure of the maleimide – formic acid dimer, showing the
hydrogen bond distances in Å......................................................................................155
13
Figure 6.4.1 Calculated B3LYP/aug-cc-pVTZ structure of the Tropolone – Formic Acid
doubly hydrogen bonded dimer. Hydrogen bond lengths are shown in Å....................159
14
LIST OF TABLES
Table 3.1.1 Mapping of asymmetric top parameters a, b and c on to rotational
constants A, B and C......................................................................................................42
Table 3.1.2 Watsons centrifugal distortion Hamiltonians for the A- and Srepresentations...............................................................................................................44
Table 3.1.3 Symmetry of rotational states for given values of Ka and Kc.....................45
Table 3.1.4 Summary of selection rules for an asymmetric top molecule. For all types
of transitions ∆J = 0, ±1..................................................................................................45
Table 4.1.1 Parent isotopologue transitions. Frequencies are given in MHz...............56
Table 4.1.2 –OD isotopologue transitions. Frequencies are given in MHz..................56
Table 4.1.3 Spectral assignments and frequencies for the high energy conformer of
the CPCA monomer. The observed – calculated (o – c) values are in kHz....................58
Table 4.1.4 Spectral assignment and frequencies for the 13C isotopologues of the
cyclopropanecarboxylic acid low energy conformer. The observed – calculated (o – c)
values are listed in kHz...................................................................................................58
Table 4.1.5 Spectroscopic constants for the high energy conformer of
cyclopropanecarboxylic acid...........................................................................................60
Table 4.1.6 Spectroscopic constants for the parent and 13C isotopologues of the
CPCA low energy conformer and the best fit structure rotational constants, all given in
MHz. Also shown are the measured – calculated (M – C) differences in the rotational
constants........................................................................................................................61
Table 4.1.7 Coordinates of the best fit low energy conformer of CPCA and the 13C
isotopically substituted coordinates, calculated by a Kraitchman analysis.....................62
15
Table 4.1.8 Interatomic distances obtained by fitting the experimental rotational
constants for six isotopologues. Bond lengths are in Å. Unreported bond lengths were
fixed at calculated B3LYP/aug-cc-pVQZ values.............................................................63
Table 4.1.9 Angles obtained by fitting the experimental and rotational constants for six
isotopologues. Angles are listed in degrees (°). The last 2 listed angles are dihedral
angles, indicating the non-planarity of carbon atoms 3 and 6. Unreported angles were
held fixed to calculated B3LYP/aug-cc-pVQZ values.....................................................64
Table 4.2.1 Results of the measurements and least squares fit calculations for CDO
parent isotopologue transitions. The standard deviation of the fit is 0.002 MHz.
Frequencies are given in MHz...................................................................................68-69
Table 4.2.2 Results of the measurements and least squares fit calculations for D-CDO
isotopologue transitions. The standard deviation of the fit is 0.005 MHz. Frequencies are
given in MHz...................................................................................................................69
Table 4.2.3 Results of the measurements and least squares fit calculations for 13C
isotopologues of 1,2-CDO. The standard deviation of each of the fits (in order of
numbering in Figure 1) are 0.002 MHz, 0.001 MHz, 0.001 MHz, 0.004 MHz, 0.001 MHz,
and 0.002 MHz. Frequencies are given in MHz..............................................................70
Table 4.2.4 Interatomic distances obtained by fitting the experimental rotational
constants for eight isotopologues. Bond lengths are in Å. Starred bond lengths(*) were
fixed at calculated (Gaussian) values.............................................................................71
Table 4.2.5 Angles obtained by fitting the experimental and rotational constants for
eight isotopologues. Angles are listed in °. The last 2 listed angles are dihedral angles,
indicating the non-planarity of the cyclohexane skeleton...............................................72
16
Table 4.2.6 MEASURED rotational constants and the “best fit” CALCULATED values
for rotational constants obtained from the structure fit, given in MHz. The centrifugal
distortional constants (DJ and DK) were obtained from the microwave fit of the parent
isotopolgue and are DJ=0.04355 KHz and DK=0.4358 KHz. The distortion constants
were held fixed to these values when obtaining the microwave fit for each of the other
isotopologues. The standard deviation for the structure fit is 0.18 MHz....................72-73
Table 4.2.7 Atom Cartesian coordinates in a, b, c system for the best fit structure of
CDO, and the Kraitchman determined values (Krait.)....................................................74
Table 5.1.1 Measured rotational transitions of the parent isotopologue of Maleimide,
shown in MHz............................................................................................................79-80
Table 5.1.2 Measured rotational transitions of each unique 13C isotopologue and the –
ND isotopologue, shown in MHz...............................................................................81-82
Table 5.1.3 Fit rotational, centrifugal distortion, and quadrupole coupling constants of
the parent, unique 13C isotopologues, and –ND isotopologue. Also shown are the
MP2/6-311++G** and B3LYP/aug-cc-pVTZ calculated values for the parent................83
Table 5.1.4 Measured rotational constants compared to the rotational constants
calculated of the best fit structure, also showing the difference (M – C), shown in MHz.
The standard deviation of the best fit structure was 0.279 MHz.....................................84
Table 5.1.5 Principle a and b coordinates (Å) of the best fit structure compared to the
coordinates of the unique singly substituted 13C substituted and –ND isotopologues
determined from a Kraitchman analysis. The Kraitchman coordinates only show the
magnitude of the substituted coordinates.......................................................................86
17
Table 5.1.6 Microwave fit values for bond lengths (in angstroms) compared to MP2/6311++G** calculated values. Corresponding bond lengths across line of symmetry are
equal...............................................................................................................................87
Table 5.1.7 Microwave fit values for angles (in degrees) compared to MP2/6311++G** calculated values. Corresponding angles across line of symmetry are
equal...............................................................................................................................87
Table 5.2.1 Measured rotational transitions of the parent isotopologue shown in
MHz...........................................................................................................................90-91
Table 5.2.2 Measured rotational transitions of each unique 13C isotopologue shown in
MHz................................................................................................................................92
Table 5.2.3 Fit rotational, centrifugal distortion and quadrupole coupling constants of
the parent and unique 13C isotopologues, as well as the MP2/6-311++G** calculated
values for the parent.......................................................................................................95
Table 5.2.4 Measured rotational constants compared to the rotational constants
calculated of the best fit structure, also showing the difference (M – C)........................96
Table 5.2.5 Principle a and b coordinates of the best fit structure compared to the
coordinates of the unique 13C substituted atoms determined from a Kraitchman
analysis......................................................................................................................97-98
Table 5.2.6 Microwave fit values for bond lengths (in angstroms) compared to
B3LYP/aug-cc-pVQZ calculated values..........................................................................99
Table 5.2.7 Microwave fit values for angles (in degrees) compared to B3LYP/aug-ccpVQZ calculated values..................................................................................................99
18
Table 5.3.1 Measured rotational transitions of the 11B14N isotopologue. Values shown
in MHz...................................................................................................................105-107
Table 5.3.2 Measured rotational transitions of the 10B14N isotopologue. Values shown
in MHz...................................................................................................................107-108
Table 5.3.3 Measured rotational transitions of the singly substituted 13C11B
isotopologues. Values shown in MHz...........................................................................110
Table 5.3.4 Measured rotational transitions of the 11B15N isotopologue. Values shown
are in MHz....................................................................................................................111
Table 5.3.5 Experimentally determined rotational, quadrupole coupling and centrifugal
distortion constants of all measured isotopologues......................................................112
Table 5.3.6 Townes-Daily determined and NBO calculated (using B3LYP/aug-ccpVTZ) electron orbital occupancies for N using sp2 hybridized orbitals. The bolded
values are the best agreement between the NBO calculation and the Townes-Dailey
analysis.........................................................................................................................114
Table 5.3.7 Townes-Daily determined and NBO calculated (using B3LYP/aug-ccpVTZ) electron orbital occupancies for B using sp2 hybridized orbitals. The bolded
values are the best agreement between the NBO calculation and the Townes-Dailey
analysis.........................................................................................................................114
Table 5.3.8 Principle axes coordinates of the best fit structure being compared with
the Kraitchman determined coordinates for each of the isotopically substituted atoms.
Values shown are in Å..................................................................................................117
Table 5.3.9 Comparison of rotational constants obtained from the best fit structure
compared with the experimentally determined values for each isotopologue and their
19
differences. The standard deviation of the structure fit was 0.151 MHz. Values shown
are in MHz....................................................................................................................118
Table 5.3.10 A comparison of B-N bond distances of BN-naphthalene and other
previously studied molecules containing the B-N bond................................................120
Table 6.1.1 Spectral assignment and frequencies for parent and 13C isotopologues of
the cyclopropanecarboxylic acid-formic acid dimer...............................................127-128
Table 6.1.2 Ab initio (MP2/aug-cc-pVTZ and B97D/aug-cc-pVTZ) spectroscopic
constants and dipole moments of the cyclopropanecarboxylic acid - formic acid
dimer.............................................................................................................................131
Table 6.1.3 Structural coordinates of the CPCA – FA (low energy) dimer in Å from the
nonlinear least squares fit with a standard deviation of 1.13 MHz. Also shown are the
Kraitchman determined coordinates for each of the isotopically 13C substituted
atoms............................................................................................................................131
Table 6.1.4 Spectroscopic constants for the parent and 13C isotopologues of the CPCA
– FA dimer....................................................................................................................133
Table 6.1.5 Interatomic distances obtained by fitting the experimental rotational
constants for six isotopologues in a nonlinear least squares fit. Hydrogen bond lengths
and COM separations are in Å.....................................................................................135
Table 6.2.1 Results of the measurements and least squares fit calculations for 1,2CDO/FA parent dimer isotopologue transitions. The standard deviation of the fit is 0.002
MHz. Frequencies are given in MHz.............................................................................140
20
Table 6.2.2 Results of the measurements and least squares fit calculations for 1,2CDO/DFA parent dimer isotopologue transitions. The standard deviation of the fit is
0.003 MHz. Frequencies are given in MHz...................................................................140
Table 6.2.3 Results of the measurements and least squares fit calculations for 1,2DCDO/FA and 1,2-DCDO/DFA dimer isotopologue transitions. Frequencies are given in
MHz. The standard deviation of the fits are 0.003 MHz and 0.002 MHz
respectively...................................................................................................................141
Table 6.2.4 Interatomic distances obtained by fitting the experimental rotational
constants for four isotopologues. Hydrogen bond lengths and COM separations are in
Å...................................................................................................................................143
Table 6.2.5 Atom Cartesian coordinates in a, b, c system for the best fit structure of
1,2-CDO/FA hydrogen bonded dimer, and the Kraitchman determined values (Krait.) for
the isotopic substitutions...............................................................................................144
Table 6.2.6 MEASURED rotational constants and the “best fit” CALCULATED values
for rotational constants obtained from the structure fit. The standard deviation for the fit
is 1.12 MHz. Also shown are the distortion constants (kHz) of the parent isotopologue,
held fixed for all other isotopic substitutions.................................................................146
Table 6.3.1 Measured rotational transitions of the maleimide – formic acid heterodimer
and the differences (o-c) from the calculated values in the fit. Values shown are in
MHz.......................................................................................................................151-152
Table 6.3.2 Measured rotational transitions of the isotopologues of the Mal-FA dimer
and the differences (o-c) from the calculated values in the fit. Values shown are in
MHz.......................................................................................................................152-153
21
Table 6.3.3 Fit rotational, centrifugal distortion, and quadrupole coupling constants of
the Mal – FA dimer. Also shown is the B3LYP/aug-cc-pVTZ calculated values...........154
Table 6.3.4 Hydrogen bond distances and center of mass separation of the monomers
in the best fit structure compared with the B3LYP/aug-cc-pVTZ calculated values,
shown in Å....................................................................................................................156
Table 6.3.5 Best fit atomic coordinates (Å) of the best fit structure compared with the
Kraitchman determined coordinates of the substituted D isotopes. The Kraitchman
values only show the magnitudes of the COM coordinates..........................................157
Table 6.4.1 Measured a- and b-type rotational transitions of the tropolone – formic
acid doubly hydrogen bonded dimer. Values are shown in MHz..................................160
Table 6.4.2 Experimental and calculated rotational constants of the tropolone – formic
acid doubly hydrogen bonded dimer.............................................................................162
Table 7.1. Optimized rotational constants for several doubly hydrogen bonded dimers
using B3LYP/aug-cc-pVTZ...........................................................................................169
22
ABSTRACT
The microwave spectra were measured in the 4-15 GHz regime for
cyclopropanecarboxylic acid, 1,2-cyclohexanedione, maleimide, phthalimide, and 4a,8aazaboranaphthalene. Doubly hydrogen bonded dimers formed with formic acid were
also measured with the molecules cyclopropanecarboxylic acid, 1,2-cyclohexanedione,
maleimide, and tropolone. Measurements were made using a pulsed beam Fourier
transform microwave spectrometer. Rotational and centrifugal distortion constants were
determined from the microwave spectra. In the case of the systems that exhibit electric
quadrupole coupling interactions, the electric quadrupole coupling strengths were also
determined from the analysis of the hyperfine structure in the spectra, yielding additional
electronic structure information for the molecules studied. The spectra were also
measured for a number of unique, singly substituted isotopologues under natural
abundance concentrations. This isotopologue data is crucial in order to obtain key gas
phase molecular structure parameters of the molecules and complexes studied. Many
theoretical computations, using ab initio and DFT methods, were also performed to
obtain optimized electronic structures of the systems studied. These computations aid in
the search and assignments of the rotational transitions measured. Comparisons
between the theory and the experimental results are described in greater detail in the
respective chapters for those systems. The experimental results for the organic systems
studied agreed well (within a few percent) with the gas phase optimization computations
performed.
23
1. INTRODUCTION
Scientific research has reached a point throughout its inspiring history that
making use of theoretical models and computational predictions for molecular systems
is of fundamental importance. These models are crucial to chemists such as in the
areas of spectroscopy, organic synthesis, or in the development of new catalysts for
important industrial applications such as hydrogen production. The high resolution that
microwave spectroscopy provides enables this technique to be an invaluable tool in
gauging the predictive power of currently existing theoretical models. The gas phase
structures determined from the microwave spectra are the best “free molecule”
representations of systems, absent of many of the types of interactions that are
observed in condensed phases. The types of molecules studied in this dissertation
cover a range of organic molecules and hydrogen bonded dimers. These systems
provide great benchmarks on which to refine the currently available theoretical methods.
The gas phase molecular structures obtained for the systems studied in this dissertation
are discussed in the following chapters.
Spectroscopy is the technique in which the energy levels of a molecule are
studied with electromagnetic radiation. The radiation excites the molecules from one
lower energy state to a higher energy state, as in the case of the absorption, or radiation
is emitted when a molecule relaxes from a higher energy state to a lower energy state.
In the case of microwave spectroscopy, or rotational spectroscopy, microwave radiation
between 1-1000 GHz is used to excite molecules that have permanent electric dipole
moments from one rotational (or ro-vibrational) state to another. Valuable information
can be gained about the systems studied by measuring the microwave spectra, such as
24
key gas phase structural parameters, electronic structure information of molecules, and
information about the dynamics of some systems, for example concerted double proton
tunneling in hydrogen bonded dimers. The microwave spectrometer used to measure
the rotational spectra of the molecules studied in this dissertation is described in greater
detail in chapter two, but will also be briefly described here. First the molecules are
pulsed into the microwave cavity maintained at low pressures of about 10-7 Torr using a
solenoid pulsed valve. The low pressure in the cavity is achieved using a mechanical
fore pump and a diffusion pump. This cavity has two spherical mirrors that can be tuned
to resonance. This resonance condition is achieved when there are an integer number
of half wavelengths of the radiation radiating between the two mirrors. The microwave
pulses are generated and then coupled to the cavity with a small quarter wave antenna
protruding from a fixed mirror. This type of microwave cavity with these two spherical
mirrors is called a Fabry-Pérot resonator. Shortly after the molecular beam is pulsed
into the cavity using the solenoid valve, a one microsecond burst of radiation is
generated at the microwave switch and is coupled into the cavity with the antenna. If the
frequency of this resonant radiation is within ± 1 MHz of a rotational transition in the
molecule, by the uncertainty principle, the sample will become coherently polarized.
After a short time the molecules will begin to relax and emit a molecular free induction
decay signal, or FID. From the recorded FID signal, a rotational transition frequency is
measured.
The theory of quantum mechanics and angular momenta describe the energy
levels and assignments of all of the rotational transitions observed in this dissertation.
The sources of angular momenta within these individual molecules can arise from the
25
rotation of the molecule, the nuclear spin, the electronic spin, and also the electronic
state of the molecule. Chapter three provides a brief description of the rotational energy
level expressions for symmetric and asymmetric top molecules as well as centrifugal
distortion corrections. Real molecules are not rigid and this distortion significantly affects
the rotational energy levels with large J and K quantum numbers. Chapter three also
discusses some of the computational details used in this dissertation, but the details
pertaining to the specific systems studied are given in their respective chapters. The
optimization of the gas phase molecular structure is one key to analyzing the microwave
spectra. Much of the time, the theoretical models used will yield rotational constants in
fair agreement with the experimental results, but that is not always the case as is
observed for some organometallic systems which may be off by 10% or more. It is
crucial to compare the experimental results from these microwave studies to that of
theory due to the importance of having accurate models to describe, for instance, the
hydrogen bonding and proton tunneling dynamics within large enzymes or in
macromolecules such as DNA. Obtaining this information about these small benchmark
systems will aid future scientific research in advancing theoretical models, as well as
provide chemists with an idea of which models accurately describe systems of interest.
The organic molecules studied in this dissertation are similar to many of the small
molecules synthesized for drug-development and used in organic synthesis. The
computational theory used in this dissertation can predict structural parameters to within
a few percent for some systems, but the larger systems become more difficult to model
with the currently available theoretical methods. This is partly due to the lack of
computational power to efficiently optimize and determine the structures of the
26
molecules using high levels of theory. Therefore it is important to study these small
organic molecules, as detailed in this dissertation, to provide these benchmarks for
theoreticians. Chapter four focuses on the results of simple organic molecules that are
considered large in the microwave spectroscopy realm. Examples of the systems
studied are cyclopropanecarboxylic acid (CPCA, Figure 1.1) and 1,2-cyclohexanedione
(1,2-CDO, Figure 1.2).
Figure 1.1
Ground state structure of cyclopropanecarboxylic acid.
Figure 1.2
Molecular structure of 1,2-cyclohexanedione in its monoenolic form.
In the case of CPCA, the microwave spectra revealed an additional excited state
conformer that had not been observed in previous microwave studies. It is important to
27
measure the spectra of the excited states of molecules as computational theory needs
to be put to the test with these excited state structures. It is also important to
characterize these excited states as some chemical reactions or enzymatic processes
may begin from only the excited state conformer of a substrate. Knowing the structures
of these high energy states is essential to determining reaction mechanisms. The study
of 1,2-cyclohexanedione revealed that the prominent structure observed in the gas
phase was a monoenolic tautomer, as opposed to the dione. The prevalence of this
tautomer indicates the enol form is lower in energy, possibly due to the intramolecular
hydrogen bond formed by the enol and the remaining ketone, which is similar to the
intramolecular interaction observed in molecules such as tropolone.
The complexity of the microwave spectra of the organic molecules studied is
increased when organic molecules have nuclei with nuclear spin greater than one half.
These nuclei have nonspherical charge distributions and quadrupole moments that
generate a measureable hyperfine structure in the microwave spectra. Chapter five
discusses the molecules that have one nitrogen nucleus (nuclear spin = 1) in two of the
molecules, maleimide and phthalimide, and 4a,8a-azaboranaphthalene where there are
both boron and nitrogen nuclei (10B and 11B both have nuclear spins of 3 and 3/2
respectively). These molecules are shown in Figure 1.3 A-C.
28
Figure 1.3
Molecular structures of A) maleimide, B) phthalimide, and C) 4a,8a-
azaboranaphthalene.
Due to these molecules exhibiting the electric quadrupole hyperfine structure,
additional electronic structure information can be gained about these systems. The
quadrupole coupling strengths determined from the analysis of the hyperfine structure
directly provide electron charge distributions. In the case of 4a,8a-azaboranaphthalene,
an extended Townes-Dailey analysis was performed to determine the numbers of
electrons in each of the nuclei’s (11B and 14N) valence hybridized orbitals, which
provides some insight into the extent of the aromatic character exhibited in this
molecule.
The pulsed beam microwave technique also provides an efficient method to form
and isolate hydrogen bonded systems in the gas phase.1 The doubly hydrogen bonded
dimers formed with formic acid, as studied in this dissertation, represent a class of
noncovalent systems whose structures may not be described very well by the
theoretical methods available. Some previously studied doubly hydrogen bonded
dimers, such as the dimer formed between formic acid and propiolic acid or benzoic
acid and formic acid, exhibit a concerted double proton tunneling motion between the
two molecules. Spectral splittings are observed in the microwave spectra caused by the
29
tunneling motion and these splittings are further analyzed to obtain information on the
dynamics of this tunneling process, such as the tunneling splitting between the two
states involved. Additional information can be deduced about the barrier height in the
potential energy surface through simple models of the potential energy surface. As
many doubly hydrogen bonded dimers exhibit the concerted tunneling motion, it is
crucial to study more hydrogen bonded dimers in order to determine the information
about the dynamics of the tunneling process. It seems that the dimers that exhibit this
tunneling motion have a C2v(M) symmetry2 or a C2v symmetry at the transition state (the
point where the two protons are equidistant between the two molecules). This symmetry
creates a symmetric double well potential energy surface that allows for the tunneling
motion to be resolved in the spectra. One question to answer is: how asymmetric can
these dimers be and still exhibit the tunneling motion? It would be very important if this
tunneling motion is observed in asymmetric dimers to gain the information about the
tunneling motion in these dimers with asymmetric potential energy surfaces. Chapter six
discusses the results obtained from the dimers studied in great detail.
30
2. RESEARCH METHODS
2.1 INTRODUCTION
The microwave spectrometers used to measure the high resolution microwave
spectra of all the molecules and complexes studied in this dissertation are Flygare-Balle
type pulsed beam Fourier transform microwave (PBFTMW) spectrometers. They have
very high resolution and sensitivity that allows for the measurement of many singly
substituted isotopologues under natural abundance concentrations. The sensitivity is so
great that a 15N singly substituted isotopologue was able to be observed in BNnaphthalene discussed in chapter 5.3. This is the largest molecule in which 15N was
observed under natural abundance. Successful experiments consist of performing
electronic structure computations to optimize the equilibrium gas phase structures
followed by introducing the molecules into the gas phase which are then pulsed into the
PBFTMW spectrometer with a Ne carrier gas by a solenoid pulsed valve. Following the
measurements, the transitions are assigned to the correct rotational energy levels to
yield very accurate rotational constants. These rotational constants obtained from the
assigned spectra are used further to determine the gas phase structural parameters of
the molecule through a nonlinear least squares fitting routine.
2.2 MICROWAVE SPECTROMETER
The PBFTMW spectrometer used in this dissertation has been developed and
reported previously.3,4 The resolution of spectrometer one (SP1) is about 10 kHz and
the frequency bandwidth covered for each stimulation frequency is about ±1 MHz, due
to the uncertainty principle. A block diagram of this microwave spectrometer is shown
31
below in Figure 2.2.1. The molecular beam, which includes the neon carrier gas and the
gaseous sample, is pulsed transversely into the Fabry-Pérot resonance cavity at a rate
of ~2 Hz. Within the Fabry-Pérot cavity, there are two spherical mirrors 30 cm in
diameter with a 60 cm radius of curvature. The microwave radiation pulse is coupled to
the cavity using a coaxial cable connected to a quarter wave antenna that lies parallel to
the mirror’s surface. The coupling of the radiation can be adjusted by modifying the
distance between the mirror and the antenna. Under the current conditions of the
spectrometer, the frequency range of 4-18 GHz is accessible to probe the molecules of
interest.
Figure 2.2.1. Block diagram of the electronics for the pulsed-beam Fourier transform
microwave spectrometer.
Once the molecular sample has been pulsed into the microwave cavity, a π/4
microwave signal is generated at about 10 dBm (~10 mW) and passed through an
attenuator to decrease the power of this signal further. A pulse of this signal is then sent
into the cavity, about 1 ms after the molecular beam is pulsed into the cavity. The
microwave pulse is generated by sending a 1 µs electrical signal to the fast microwave
32
switch triggering it, allowing for a 1 µs burst of radiation to couple into the cavity. When
the mirrors are tuned to resonance for a specific stimulation frequency, the microwave
radiation will resonate between the mirrors and if the stimulation frequency is close to
the rotational transition frequency of the molecule (± 1 MHz due to the uncertainty
principle), the molecules pulsed into the cavity will be coherently polarized in the
resonant electromagnetic beam. After the stimulating microwave pulse decays, the
molecular emission signal caused by the relaxation of the coherently polarized sample
(free induction decay or FID) is collected for ~100 µs and allowed to pass through a
homodyne detection system. The molecular signal is passed through an amplifier
(shown as 4-8 GHz in Figure 2.2.1) and mixed with the synthesized stimulation
frequency. The mixed signal is passed through a 0-1 MHz amplifier, digitized at 5 MHz,
and the FID is recorded with a PICO scope (a multichannel analog to digital converter)
that is displayed on the computer through the data collection program which displays
the average signal collected. The computer subsequently will perform a Fourier
transform on the measured FID to obtain the data in the frequency domain. Successful
measurements of rotational transitions depend heavily on the delays between each of
the electrical signals that activate the valve, microwave switch and FID data collection.
The sequence of each of the pulses in the spectrometer design can be seen in Figure
2.2.2. The top trace shows the signal sent to the solenoid pulsed valve and after the 1
ms delay (indicated by the green dashed line) the short microsecond transmit signal is
sent to the microwave switch (bottom trace) that allows the coupling of the radiation into
the cavity. After the microwave pulse decays (indicated by the receive delay shown by
33
the spacing between the blue and red lines) the signal to begin data collection begins
(middle trace).
Figure 2.2.2. Pulse sequence of spectrometer. The valve opens and after a 1 ms delay,
a short 1 μs pulse of microwave radiation is sent through the microwave switch and the
radiation fills the cavity. After a short time, the PICO scope is triggered and 100 μs of
data is collected.
To find the resonant mode of the mirrors for a specific stimulating frequency, the
reflected signal out of the cavity is monitored using a directional coupler and recorded
using a standard 2 channel oscilloscope (Figure 2.2.3). At a given stimulation
frequency, a DC motor operated by the user moves the mirrors until the cavity is in
resonance. The resonant condition is determined by a decrease in reflected signal
recorded from the microwave cavity. The decrease in reflected signal occurs when there
are an integral number of half wavelengths of the radiation between the two mirrors.
The Q-values, or quality values (f / ∆f), for the resonant condition in the microwave
spectrometer are on the order of 30000, indicating a high quality resonant cavity.
34
Figure 2.2.3. Diagram showing directional coupler used to monitor reflected microwave
signal.
To more efficiently scan frequency ranges of the rotational transitions predicted,
an automatic scan program was developed previously for the instrument, called
AutoScan 6.0.5 The AutoScan program allows the computer to control an HP 8673E
frequency synthesizer through its general purpose interface bus (GPIB) and track the
resonant condition by monitoring the reflected signal. The reflected signal is integrated
by a simple op-amp circuit and the integrated signal is sent to the AutoScan program
and the minimum reflected signal is found, indicating the cavity is in resonance. To set
up the AutoScan program to scan a desired frequency range, the input file is created to
contain the starting and ending frequencies. The starting frequency is entered into the
HP frequency synthesizer, the resonant condition is found manually, and the program is
initiated. The program will undergo a specific number of pulsed beam cycles for a given
stimulating frequency, which is also dictated in the input script file. Once the number of
35
pulses has been met, the program will save the file with the given frequency as the file
name and then will move the mirrors slightly, depending on the voltage supplied to the
DC motor. The frequency sweeps 1 MHz to find the minimum reflected signal and the
frequency is set that corresponds to the minimum. The voltage to the motor is adjusted
at a potentiometer control to allow the step sizes in stimulating frequency to be about
200 to 300 kHz, sufficient to save multiple FIDs of one rotational transition. To analyze
the files saved during an AutoScan sequence, two complementary programs, written in
LabVIEW, have also been previously developed for the research lab. Following the
analysis of the data with the LabView programs, the rotational transitions are measured
manually to obtain more accurate transition frequencies.
2.3 SAMPLE PREPARATION
Many of the molecules studied were purchased and transferred to a specialized
glass sample cell that was designed for the lab. This specialized glass cell is shown
below in Figure 2.3.1. Once the sample has been carefully transferred into the cell, the
cell is connected to the solenoid pulsed valve with a small piece of Tygon tubing or a
Swagelok adapter with Teflon ferrules, depending on what temperature the sample and
pulsed valve need to be heated to obtain sufficient vapor pressure of the sample. If the
temperature exceeds 50 °C, then the Swagelok adapter is used.
36
Figure 2.3.1. Specialized glass sample cell used for the microwave experiments in this
dissertation.
In the case of some molecules studied, singly deuterated isotopologues were
synthesized. These were created by mixing the sample with a deuterated solvent (either
D2O or MeOD) for a few days and the remaining solvent was pumped off under reduced
pressure. The deuterated sample was then transferred to the sample cell and the
experiment was performed as described.
37
3. THEORY AND COMPUTATIONS
3.1 THEORY
The rotational quantum number assignments of all the transitions measured in
this dissertation can be described with quantum mechanics and the angular momenta
within a molecule. The following description will not present all of the mathematics
involved in the derivation of rotational energy levels, but will show the important
quantum mechanical steps and the final results obtained. The derivations of all solutions
presented here are given in great detail in texts by Gordy and Cook6 and Kroto.7 The
program SPCAT8 by Dr. Herb Pickett was used to simulate the microwave spectra from
the optimization computations. After correctly assigning the rotational energy levels to
the transitions measured, these transitions are fit using SPFIT to a set of rotational and
centrifugal distortion constants. In the case of the molecules with the electric quadrupole
interactions, a set of quadrupole coupling strengths are also determined.
3.1.1 SYMMETRIC TOP ENERGY LEVELS
For a molecule rotating about its center of mass, the generic rotational
Hamiltonian can be written as shown below in equation 3.1. The bold letter J represents
the quantum mechanical operator for the angular momenta and Ia, Ib, Ic are the
moments of inertia with respect to the principal axes in the molecule.
(eq. 3.1)
The components of the angular momenta all lie along the principal axes (denoted a, b,
and c). The rotational constants (A, B, and C) are then conveniently defined as:
38
(3.2a)
(3.2b)
(3.2c)
In the case of a prolate symmetric top, the angular momenta along the b and c
principal axes are equivalent. The Hamiltonian can be conveniently written in terms of
rotational constants A and B shown in equation 3.3a. After operating on the rotational
wavefunction, the energy level expressions are obtained in terms of quantum numbers J
and K.
,
,
(3.3a)
The other symmetric top case is when the angular momenta along the a and b
principal axes are equivalent and this is called an oblate symmetric top. Again, the
Hamiltonian can be written in terms of rotational constants B and C shown in equation
3.3b. After operating on the rotational wavefunctions, the energy level expressions are
obtained in terms of the quantum numbers J and K.
,
,
(3.3b)
The quantum mechanical angular momentum operators Ĵ2 and Ĵa have
eigenfunctions which are the associated Legendre polynomials and these
eigenfunctions are written in Dirac notation in terms of the quantum numbers J, K, and
M as shown in equation 3.4a.
|Ψ
|JKM
39
(3.4a)
For a symmetric top, K represents the projection of the total angular momentum
of the molecule on to the symmetry axis (the a-principal axis for a prolate symmetric top
and the c-principal axis for an oblate symmetric top). M is the projection of the total
angular momentum on to the laboratory axis, which is usually labeled as z. The
projection of the angular momenta on the laboratory axis, M, is important when external
electric fields are applied to systems during Stark microwave experiments. These Stark
experiments are used to determine electric dipoles of molecules. The eigenvalues for
each of the quantum mechanical operators of angular momentum used to derive the
rotational energy levels are shown in equations 3.4b-d.
JKM JKM
1 (3.4b)
JKM JKM
(3.4c)
JKM JKM
(3.4d)
The energy levels for the two symmetric tops can then be derived from equations
3.3 and the eigenvalue results of 3.4b-d. The energy level expressions for the prolate
and oblate symmetric top molecules are then written in terms of the rotational constants
and the rotational quantum numbers, J and K, shown in equations 3.5a and b.
1
(3.5a)
1
(3.5b)
The selection rules for the transitions observed for a rigid symmetric top are ∆J =
±1 and ∆K = 0. These can be derived from the dipole moment matrix elements which
will not be discussed here. The change in J can be rationalized in terms of photons
possessing unit angular momentum. The selection rule ∆K = 0 can be explained due to
40
the symmetric top molecules not having a component of the permanent electric dipole
perpendicular to the symmetry axis to generate a torque about the axis by interaction
with the microwave radiation. There are similarities with the spectrum obtained from a
linear molecule, in that the spacing between each transition is equal to 2B. Molecules
are, however, not rigid and undergo centrifugal distortion effects that are proportional to
J and K and so the spacing between transitions are not uniform. The deviations in the
energy levels introduced by centrifugal distortion are very small and are determined
using perturbation theory methods, which will be discussed in the following sections.
3.1.2 ASYMMETRIC TOP ENERGY LEVELS
In the case of the asymmetric top molecule, all components of the angular
momenta are not equal and so the rotational Hamiltonian cannot be expressed in simple
terms of J2 and only one of the components of J. If the asymmetric top is very close to
one of the symmetric top limits, then it is useful to write the rotational Hamiltonian in a
form that takes advantage of the near symmetric top symmetry. The rotational
Hamiltonian for the asymmetric top can then be written as shown in equation 3.6 in
which a, b, and c are just parameters related to the rotational constants, depending on
the symmetry of the molecule.
(3.6)
The Hamiltonian can then be rewritten in terms of raising and lowering operators shown
in equation 3.7,
(3.7)
41
where
,
, and
. It is important to know whether
the molecule is near-prolate, near-oblate, or very asymmetric as the rotational constants
(A, B and C) can be mapped on to a, b and c in six possible ways, but it is useful to use
the following mappings listed in Table 3.1.1 in order to facilitate the diagonalization of
the Hamiltonian matrix to obtain the rotational energy levels.
Table 3.1.1 Mapping of asymmetric top parameters a, b and c on to rotational
constants A, B and C.
Parameter
a
b
c
Near-Prolate
B
C
A
Very Asymmetric
C
A
B
Near-Oblate
A
B
C
In order to solve for the energy level expressions using equation 3.7, the
following eigenvalues are needed for the associated operators shown in equations 3.8ad.
JK JK
JK JK
1 (3.8a)
(3.8b)
JK
2 JK
1
1
2 (3.8c)
JK
2 JK
1
1
2 (3.8d)
The Hamiltonian matrix for the asymmetric top has dimensions of (2J+1) by
(2J+1) due to the degeneracy in J. There are also off-diagonal components that mix Kstates that are different by ± 2. The matrix is also symmetric along both of the
diagonals, due to the degeneracy in ± K. The rotational Hamiltonian then lends itself to
42
be transformed to a new representation, using the Wang transformation described in the
texts by either Kroto or Gordy and Cook. The resulting basis functions are shown in
equation 3.9 after performing the Wang transformation.
√
| | (3.9)
Following the Wang transformation and further factorization to diagonalize the
Hamiltonian matrix yields rotational energy levels that require a new designation
different than just the two quantum numbers J and K as used for the symmetric tops.
The new energy levels are assigned to J, Ka, and Kc where J is the total angular
momentum of the molecule, Ka is the projection of the angular momentum on to the aprincipal axis (or Kprolate) and Kc is the projection of the angular momentum on to the cprincipal axis (or Koblate). The energy levels are obtained in closed form for small values
of J, but the solutions for these asymmetric tops require numerical methods for large
values of J.
3.1.3 CENTRIFUGAL DISTORTION CORRECTIONS
The molecules studied in this dissertation are not rigid and undergo distortions
due to the centrifugal force of the rotating molecule. These distortions within the
molecules depend on the quantum numbers J and K. Because molecules are not rigid,
this requires corrections to the energy levels derived in the previous sections. Watson
proposed two reduced representations to account for these distortion effects, which are
the asymmetric (A) and symmetric (S) representations. The terms in the Hamiltonian
due to these effects are listed in Table 3.1.2. Pickett’s SPCAT and SPFIT programs
take into account both of these representations, depending on the molecule and which
43
is specified. For the molecules studied in this dissertation, all were asymmetric and the
A-representation was used to determine the spectroscopic constants in the fitting of the
microwave spectra to obtain the rotational and centrifugal distortion constants.
Table 3.1.2 Watson’s centrifugal distortion Hamiltonians for the A- and Srepresentations.
Watson’s S-reduced Hamiltonian (
)
2
Watson’s A-reduced Hamiltonian (
Δ
Δ
Φ
)
Δ
Φ
Φ
Φ
2
3.1.4 MICROWAVE SELECTION RULES
Spectroscopy involves measuring the differences between energy levels to gain
information about the molecules of interest. In the case of microwave spectroscopy, the
energy levels probed are the rotational states of the molecule. In order for a rotational
transition to be excited, the permanent electric dipole moment within the molecules
needs to be nonzero. Depending on which dipole-moment matrix elements are nonzero,
there can be a-, b-, or c-type transitions, or a combination of all depending on which
dipole moment components are nonzero. The allowed transitions can be determined by
the symmetries of the wave functions of the two rotational states involved and the
44
symmetry of the dipole moment matrix elements by the cross product
Γ Ψ ΧΓ μ ΧΓ Ψ" . The rotational states and dipole moment matrix elements that
result in the totally symmetric irreducible representation A are said to be allowed. Table
3.1.3 lists the symmetries of the rotational states for given values of Ka and Kc.
Table 3.1.3 Symmetry of rotational states for given values of Ka and Kc.
Kc
Even
Odd
Odd
Even
Ka
Even
Even
Odd
Odd
Symmetry
A
B1
B2
B3
The selection rules on J, Ka, and Kc are summarized in Table 3.1.4 which give the totally
symmetric (A1) cross product between the rotational states and the dipole moment
matrix elements.
Table 3.1.4 Summary of selection rules for an asymmetric top molecule. For all types
of transitions ∆J = 0, ±1.
Dipole Moment
Component
µa ≠ 0
µb ≠ 0
µc ≠ 0
∆Ka
∆Kc
0, ±2, …
±1, ±3, …
±1, ±3, …
±1, ±3, …
±1, ±3, …
0, ±2, …
3.1.5 NUCLEAR SPIN ANGULAR MOMENTUM
In the case of closed-shell molecules that have nuclei with nuclear spin > ½, the
nuclear spin has an angular momentum that couples with the total angular momentum
of the molecule. These nuclei have quadrupole moments and this creates a
45
nonspherical charge distribution around that nucleus. The nonspherical charge
distribution interacts with the electric field gradient of the molecule as the molecule
rotates and splits each of the rotational transitions into what is called the hyperfine
structure in the microwave spectra. In the case of nuclei with spin ≤ ½, these nuclei are
spherically symmetric and thus do not interact with the electric field gradient in the
molecule. The Hamiltonian for the electric quadrupole interaction that gives rise to the
hyperfine structure in the microwave spectra is shown below in equation 3.10, which is
obtained from the Taylor expansion of the potential energy. Q is the nuclear quadrupole
moment tensor and V is the electrostatic field-gradient tensor at the nucleus generated
from the electrons in the molecule.
∑
(3.10)
The first term from the Taylor expansion of the potential energy represents the
nuclear monopole and does not interact with the electric field during the molecular
rotation. The second term represents the nuclear dipole and this can be neglected.
External electric fields allow the molecular dipole to align with the applied electric field
and gives rise to what is known as the Stark effect which introduces additional spectral
splittings dependent on the laboratory axes. The Stark effect in rotational spectroscopy
is useful for the determination of the molecular electric dipole moments. The third term
from the Taylor expansion of the potential energy (eq. 3.10) gives rise to the interaction
of the quadrupole moment of the nuclei and the electric field around the nuclei. Vij(2) and
Qij(2) are second rank symmetric tensors that represent the electric field gradient of
electrons in non-spherically symmetric orbitals and the nuclear charge distribution.
Expanding the above equation and collecting terms yields equation 3.11, shown below
46
for the electric quadrupole Hamiltonian. Q is the quadrupole moment of the nucleus and
qJ is the electric field gradient of the molecule averaged over the ro-vibrational state
involved. I is the angular momentum resulting from the nuclear spin and J is the total
angular momentum in the molecule.
3
∙
∙
(eq. 3.11)
Analyzing the hyperfine structure in the rotational spectra of the molecules that
exhibit these electric quadrupole interactions allows one to determine additional
electronic structure information about the molecule. The quadrupole coupling strengths
obtained from the analysis directly yield the electron distribution around these nuclei
and can be used to understand processes such as chemical bonding or reaction rates.
These parameters also supply the theoretical chemist and physicists with stringent
experimental parameters on which to refine theoretical methods. The calculated
parameters obtained from the theory can be different by 50% or more for some nuclei.
3.2 COMPUATIONAL METHODS
Electronic and molecular structure computations are a crucial aspect to the
research performed in this dissertation and the importance of such computations is
increasing in every aspect of chemistry, physics, and biology. In order to predict the
microwave spectra, the structures of these molecules first needs to be predicted, from
which moments of inertia and rotational constants can be calculated. From the
optimized structures of the molecules, the center of mass is determined and the
moments and products of inertia are calculated using equations 3.12-3.17. For the off
diagonal products of inertia, Ixy is equal to Iyx because the tensor is symmetric. The
47
inertia tensor is then diagonalized using the secular equation and the diagonal
components are then equal to the moments of inertia in the molecular principal axis
system – from which the rotational constants of the molecule A, B, and C are
determined and used to calculate the energy of the rotational levels.
∑
(eq. 3.12)
∑
(eq. 3.13)
∑
(eq. 3.14)
∑
(eq. 3.15)
∑
(eq. 3.16)
∑
(eq. 3.17)
Another way to determine the diagonal moment of inertia tensor is to find the set
of Euler angles to rotate the original inertia tensor into the principal axis system yielding
the diagonalized inertia tensor. However, since the inertia tensor can be easily
diagonalized and the principal moments determined using the secular equation, these
Euler angles can be found with the equation R-1IR = I’, where R is the 3x3 rotation
matrix, R-1 is its inverse, I is the non-diagonal 3x3 inertia tensor and I’ is the
diagonalized inertia tensor. One can compute the three angles given the three principal
moments of inertia from the diagonalization process. The description of this method is
given in great detail in the text by Gordy and Cook.
The microwave spectra is then simulated using Pickett’s SPCAT program with
the calculated rotational constants from the optimized equilibrium gas phase structure’s
48
diagonal inertia tensor. However, for most molecular systems of interest (more than a
few atoms) the exact solutions to the Schrödinger equation cannot be obtained and so
obtaining molecular structures with the lowest possible energy becomes quite difficult.
The time for each computational method to optimize the electronic structures depends
on the number of electrons in the system. Ab initio methods such as MP2 and coupled
cluster (CC) scale as N5 and N7 where N is the number of electrons.9 These methods
sometimes produce more accurate results when compared with density functional
theory (DFT) methods, which scale as N4 and so the results are obtained faster. The
speed of DFT computations comes from the way in which electron correlation is
handled when solving for the energies. DFT methods assume that the electron density
does not vary rapidly throughout the molecule.
Several systems were studied in this dissertation where both MP2 and DFT
methods produced similar results and sometimes the DFT methods were closer to the
experimentally determined values. All of the computations were performed on the highperformance computing system at the University of Arizona using the Gaussian 09
suite.10 Details on the electronic structure computations performed for each of the
specific systems studied will be given in the respective chapters for those systems. A
brief overview of the optimization procedure follows.
To begin the gas phase optimization computations on the molecular species of
interest, these systems first need to be constructed in molecular modeling programs.
Any molecular modeling software can be used, so long as Cartesian coordinates or a Zmatrix of the molecular structure is obtained. These preliminary structures should be
built with some chemical intuition – for example a trans-species is typically lower in
49
energy than its cis counterpart and so if the ground state is desired, the trans-structure
is constructed. This is an important step in the optimization of the molecular systems
studied as the structures may be optimized to a local minimum in the potential energy
surface as opposed to the global minimum which is desired. Following the construction
of the molecular species, the Cartesian coordinates or Z-matrices are used in the
Gaussian input file with a specific formatting, shown in the appendix. If a potential
energy scan is required for the system, a Z-matrix must be used in order to specify
which structural parameters to vary (either bonds, angles, or dihedral angles) – the
keywords and examples of these types of calculation are documented well on the
Gaussian corporation website. A script file is then created in order to submit the
computation to the HPC system at the University of Arizona, also shown in the
appendix. The computational power, such as memory and number of nodes, is specified
in this script file, as well as the location and name of the input file with the molecular
coordinates or Z-matrix.
3.3 LEAST SQUARES STRUCTURE FITTING
The most valuable piece of information that can be determined of molecules by
measuring the microwave spectra is the determination of key gas phase molecular
structure parameters. These parameters are obtained by measuring the microwave
spectra of many singly substituted isotopologues, from which the rotational constants
are determined by fitting the assigned spectra using Pickett’s SPFIT program. The
rotational constants of the most abundant isotopic species and all of the unique singly
substituted isotopologues are used in an iterative Fortran program (shown in the
50
appendix) to determine the important molecular structure parameters. For the
isotopologue spectra measured for the molecules described, these isotopic species
were measured under natural abundance concentrations.
First the molecular geometry is obtained either from the electronic structure
computations or from X-ray crystal structure data published in the literature. The
Cartesian coordinates of the atoms are parameterized and the best values of these
parameters are obtained through a nonlinear least squares method. The best fit
structure obtained using this structure fitting program has calculated rotational constants
closest in value to all of the experimentally determined values obtained from the
assigned spectra. A standard deviation is reported for the molecular structure fit
obtained and is shown below in equation 3.12.
∑
(eq. 3.12)
Yi is the set of experimental rotational constants for each of the isotopologues
and Ycalc are the calculated values from the best fit structure (with the smallest sum of
squares). N is the number of rotational constants determined from the observed
microwave spectra for all of the isotopologues measured and P is the number of
parameters used to adjust the Cartesian coordinates of the molecular structure.
Once the molecular structure is obtained from the fitting routine, the coordinates,
with respect to the molecule’s center of mass, are calculated for each of the singly
substituted atoms using the Kraitchman equations, which are described well in the text
by Gordy and Cook. These Kraitchman calculated substitution coordinates are
51
compared with the coordinates obtained from the structure fit and the obtained structure
is typically accurate to about 0.01 Å and sometimes even better.
52
4. MICROWAVE MEASUREMENTS AND STRUCTURES OF LARGE ORGANIC
MOLECULES
The computational power of current theoretical models decreases in accuracy as
the size of the molecules and complexes become larger. Current models scale as a
power of the number of electrons within the systems, so it is important to study large
molecules and weakly interacting complexes to gauge the accuracy of the currently
available theory. The measurement of the microwave spectra of the organic molecules
discussed in this chapter aim to provide benchmarks for the theoreticians in order to
improve upon the existing theory.
Cyclopropanecarboxylic acid is a carboxylic acid with a cyclopropane ring. Even
though it is considered small on most standards, the ability of current available
computational methods are still unable to calculate extremely accurately what is
observed in the laboratory. Furthermore, molecules like cyclopropanecarboxylic acid
undergo some internal motion and excited state conformers are sometimes observed,
which was the case for this carboxylic acid. 1,2-cyclohexanedione is another somewhat
large molecule and provides another great benchmark for theoretical methods. The
case of 1,2-cyclohexanedione was also an interesting one, in that under the
experimental conditions the molecule seemed to have completely tautomerized to its
monoenolic tautomer, which was observed. Tautomeric species and other
conformations, such as the one observed for 1,2-cyclohexanedione, may be elusive and
difficult to study by other methods. Microwave spectroscopy lends itself as a great
technique to obtain free molecular structure parameters, as well as to observe the
dynamics and other elusive excited state structures or complexes.
53
4.1 CYCLOPROPANECARBOXYLIC ACID
4.1.1 INTRODUCTION
Derivatives of cyclopropanes are versatile compounds in many organic
syntheses and are found throughout nature.11 Specifically, cyclopropanecarboxylic acid
(CPCA) is an important biologically active compound due to the hypoglycemic metabolic
effects shown in experiments by Duncombe and Rising in several animal species,
including humans.12 CPCA can be synthesized using chiral copper carbenoids13 and
due to the versatility of the cyclopropane ring, geminal dihalides of CPCA can be easily
derivatized using a Ni induced reductive carbonylation.14 Other syntheses of CPCA
utilize transition metal catalyzed reactions, cycloaddition of alkenes, sulfoxides and
other metal carbenoids.
Potential energy scans of the different conformers of CPCA have been previously
performed and predicted, at room temperature, the abundances of the two conformers
of CPCA. These conformers were separated in energy by only a few hundred
wavenumbers. The predicted abundances from these initial calculations were 85% and
15% for the lower and higher energy conformers, respectively.15 Additional calculations
were performed and these predicted a difference in energy of only 321 cm-1, so it is
reasonable that rotational transitions from the excited state conformer should be
observed. In the work by Marstokk et al., the high energy conformer was searched for in
the 26.5-38.0 GHz range but was not observed, most likely due to the low abundance of
the species in addition to the low populations of the large J energy levels. In this study
described here, the microwave measurements and determined spectroscopic constants
of the low and high energy conformers of CPCA are reported.
54
The crystal structure of CPCA was determined by Boer and Stam.16 IR and
Raman spectroscopic techniques were utilized by Maillols, Tabacik, and Sportouch17 to
determine some gaseous structural parameters of CPCA. To extend the study on
gaseous CPCA, Marstokk, Møllendal, and Samdal18 performed an electron diffraction
experiment, waveguide microwave measurements (in the 26.5-38 GHz regime), and ab
initio computations. In this study presented here, high resolution pulsed-beam Fouriertransform (PBFT) microwave spectroscopy was used to measure low frequency
transitions for the low energy conformer (in the 5-15 GHz regime) of the parent, the
unique singly substituted 13C isotopologues, and the –OD isotopologue and key gas
phase structural parameters were determined. Additional transitions were also
measured and assigned corresponding to the excited state conformer.19,20
4.1.2 MICROWAVE MEASUREMENTS
The CPCA sample was purchased from Sigma Aldrich (95%) and was used as
received. The deuterated CPCA sample was prepared by mixing equimolar quantities of
CPCA (Sigma Aldrich, 95%) and MeOD, or deuterated methanol, (Cambridge Isotope
Lab, Inc., 99%) and allowing the H and D to exchange overnight. The remaining MeOH,
after the exchange, was removed from the mixture under reduced pressure, leaving the
less volatile CPCA-OD behind. Each sample was then transferred into a specialized
glass sample cell presented in chapter two. The sample and pulsed-valve (General
Valve, series 9) were heated to 45 °C to obtain sufficient vapor pressure of the molecule
to provide a strong test signal. The pressure within the microwave cavity was
maintained at 10-6 to 10-7 Torr prior to the pulsed injection of the sample and Ne carrier
55
gas. The Ne backing pressure was maintained at ~1 atm during microwave
measurements.
Table 4.1.1 Parent isotopologue transitions of CPCA. Frequencies are given in MHz.
J′Ka’ Kc’
625
101
110
202
211
312
624
413
413
514
212
111
202
211
303
313
J″Ka” Kc”
532
000
101
111
202
303
533
322
404
505
111
000
101
110
212
212
obs
o-c
5039.365
5106.835
5242.984
5296.063
5603.069
6175.152
6210.009
6878.550
6995.124
8104.475
9870.926
10007.086
10196.314
10556.397
10676.475
14795.766
0.000
-0.006
0.001
-0.001
0.001
-0.001
0.000
-0.001
-0.001
0.000
0.002
-0.002
0.003
0.002
0.001
-0.002
Table 4.1.2 –OD isotopologue transitions of CPCA. Frequencies are given in MHz.
J′Ka’ Kc’
101
110
211
312
413
514
212
202
211
J″Ka” Kc”
000
101
202
303
404
505
111
101
110
obs
o-c
4938.008
5311.345
5647.302
6178.926
6937.507
7960.020
9555.002
9860.989
10196.945
0.009
0.001
-0.009
0.005
0.003
0.001
0.012
-0.002
-0.014
Microwave transitions were measured for the parent isotopologue and the –OD
isotopologue in the 5-15 GHz range using a PBFT Flygare-Balle type microwave
spectrometer described in chapter two. 16 new transitions have been measured for the
56
parent and 9 for the –OD isotopologue corresponding to the CPCA molecule shown in
Figure 4.1.1 (top). The newly measured rotational transitions for the parent and –OD
isotopologues are given in Tables 4.1.1 and 4.1.2 respectively. Additional
measurements on the lower energy CPCA conformer, were extended to include all of
the unique single 13C substituted positions, with all transitions being measured under
natural abundance concentrations. These measured rotational transitions are shown in
Table 4.1.4. The numbering scheme for each of the substituted atoms reflects what is
shown in Figure 4.1.1. These new 13C measurements were taken at room temperature,
as a parent test signal was a very strong after pulsing at a higher temperature (60 °C).
Measurements on the higher energy CPCA conformer, corresponding to the
geometry of the CPCA molecule shown in Figure 4.1.1 (bottom), were also taken at
room temperature after ~2 hours of pulsing the CPCA sample through the pulsed valve
at ~60 °C. The measured transitions of this new conformer are shown in Table 4.1.3.
Figure 4.1.1 Structures of the two conformers of CPCA where the top is lower in
energy by 373.1 cm-1, obtained from the B3LYP/aug-cc-pVQZ calculation.
57
Table 4.1.3 Spectral assignments and frequencies for the high energy conformer of
CPCA. Frequencies given in MHz.
J'
1
1
2
2
3
4
1
2
2
2
Ka'
1
0
1
0
1
1
1
1
0
0
Kc'
0
1
1
2
2
3
1
2
2
2
J''
1
0
2
1
3
4
0
1
1
1
Ka''
0
0
0
1
0
0
0
1
0
1
Kc''
1
0
2
1
3
4
0
1
1
0
Frequencies (MHz)
5037.232
5204.936
5433.717
5725.706
6068.218
6984.654
9867.375
10035.056
10388.154
10784.644
o-c
-0.004
0.004
0.006
-0.004
0.004
-0.005
-0.004
-0.002
-0.004
0.010
Table 4.1.4 Spectral assignment and frequencies for the 13C isotopologues of CPCA.
The observed – calculated (o – c) values are listed in kHz.
J' Ka' Kc' J'' Ka''
1
0
1 0
0
2
0
2 1
1
1
1
0 1
0
2
1
1 2
0
1
1
1 0
0
2
0
2 1
0
2
1
1 1
1
13
Kc''
C(3&6)
0
5027.498
1
5152.397
1
5212.357
2
5553.572
0
9914.347
1 100039.255
0
13
13
o-c*
C(9) o-c*
C(1)
2
5092.480
-4 5095.068
-2
5259.474
2
1
5249.158
0 5203.388
-1
-3 10000.827
1 9952.100
2 10167.814
0 10172.253
10536.453
o-c
2
4
-4
4
-3
4.1.3 CALCULATIONS
Since previous microwave work was previously performed by Marstokk et. al.,
the rotational constants obtained in the previous study were used to predict the lower
frequency microwave transitions. Measurements of the new experimental transitions
were in excellent agreement with the predictions from the initial study. The OD and 13C
transitions were predicted by changing the mass of the H or C atom in the initial
optimized structure to that of D or 13C, from which preliminary rotational constants of the
isotopologues were calculated. The ratios between the calculated rotational constants
58
from the theory and the experimentally determined rotational constants of the parent
isotopologue were used as scale factors and multiplied by the calculated isotopologue
rotational constants. These corrected values provided an accurate set of rotational
constants for the OD and 13C isotopologues to predict the transitions.
Potential energy scans of the rotation of the carboxylic acid moiety about the C1
– C9 bond of the CPCA monomer were previously performed, resulting in the calculated
abundances of each conformer to be 85% and 15% at room temperature. Additional
optimization calculations using B3LYP/aug-cc-pVQZ of the two conformers were also
performed and the energy difference between the conformers was calculated to be
373.1 cm-1, with the bottom conformer in Figure 4.1.1 having higher energy. The
calculated a and b dipoles of this high energy conformer were 2.02 and 1.13 D
respectively, so both a and b type transitions were expected to be observed, however
the transitions will be weak due to the lower abundance of the higher energy conformer.
The calculated values of the rotational constants from the B3LYP calculation compared
to the experimentally fit values of this high energy conformer are shown in Table 4.1.5.
59
Table 4.1.5 Spectroscopic constants for the high energy conformer of
cyclopropanecarboxylic acid.
A/MHz
B/MHz
Experiment
7452.3132(57)
2789.8602(43)
C/MHZ
2415.0725(40)
∆J/kHz
0.29(53)
∆JK/kHz
2.5(12)
N
10
σ/kHz
5
B3LYP/aug-cc- Calculation15
pVQZ
7490.121
7451
2770.327
2786
2399.7699
2411
4.1.4 ROTATIONAL CONSTANTS
The fits to obtain the rotational constants of all species were performed using
Pickett’s SPFIT program and these results are listed in Table 4.1.6. During the fit of the
13
C transitions, the centrifugal distortion constants were held fixed to the values
obtained by Marstokk et al, due to these constants being thought to be more accurately
determined with the measurement of high J and K transitions. Also in Table 4.1.6 are
the rotational constants of the best fit structure and the deviation of these constants of
the best fit structure from the experimentally determined values (M – C). The calculated
rotational constants of the best fit structure had a standard deviation of 0.31 MHz when
compared to the experimentally determined values, which is very good when taking into
consideration the magnitudes of the rotational constants of CPCA. The previously
calculated rotational constants were within <1% of the experimentally fit values and the
rotational constants obtained from the current B3LYP/aug-cc-pVQZ were in fair
agreement.
60
Table 4.1.6. Spectroscopic constants for the CPCA low energy conformer from the
experiment and the structure fit, shown in MHz.
ISOTOPOLOGUE
Parent
A
B
C
-OD
A
B
C
13
C3
A
B
C
13
C6
A
B
C
13
C9
A
B
C
13
C1
A
B
C
MEASURED
7625.0432(17)
2724.7672(8)
2382.0755(5)
7619.8580(64)
2629.4700(14)
2308.5301(14)
7563.3591(16)
2676.4756(9)
2351.0216(1)
7563.3591(16)
2676.4756(9)
2351.0216(1)
7624.9982(19)
2716.6267(19)
2375.8584(19)
7577.7505(38)
2720.6834(22)
2374.3843(28)
CALCULATED
7625.5604
2724.9594
2382.2998
7619.5759
2629.0129
2308.0919
7563.3012
2676.4388
2350.9624
7563.3063
2676.3973
2351.0214
7624.9659
2716.7176
2375.9405
7577.6578
2720.9473
2374.5590
(M – C)
-0.5172
-0.1922
-0.2243
0.2821
0.4571
0.4382
0.0579
0.0368
0.0592
0.0528
0.0783
0.0002
0.0323
-0.0909
-0.0821
0.0927
-0.2639
-0.1747
4.1.5 MOLECULAR STRUCTURE
A nonlinear least squares structure fit was performed on the low energy
conformer of CPCA using the rotational constants of all the measured singly substituted
isotopologues to obtain key gas phase structure parameters within the cyclopropane
ring. In the least squares fit, there were 8 total varied parameters in 3D Cartesian
space. 3 of these varied parameters were the movement of C3, H4 and H5 (as one
group), 3 were the movement of C6, H7 and H8 (as a second group), and 2 were the
movement of C1 and H2 (as a third group) in the a-b plane. Atoms 9-12 were all held
fixed to the calculated B3LYP/aug-cc-pVQZ coordinates. C1 and H2 were constrained
to be in the a-b plane because the c-coordinates in the calculated structure were very
small, indicating these atoms lie mostly within the a-b plane. The standard deviation of
61
this nonlinear least squares structure fit was 0.31 MHz. A Kraitchman analysis was also
performed using the Kiesel KRA program21 on the low energy CPCA monomer of all the
measured isotopologues. The best fit coordinates of the low energy CPCA conformer
are shown with the Kraitchman calculated coordinates in Table 4.1.7. Agreement
between the structure fit and the Kraitchman calculated values is very good, indicating
the best fit structure is a reasonable representation of the molecule in its ground state.
Table 4.1.7 Coordinates of the best fit low energy conformer of CPCA and the 13C
isotopically substituted coordinates, calculated by a Kraitchman analysis.
Atom
C1
H2
C3
H4
H5
C6
H7
H8
C9
O10
O11
H12
a
0.523764
0.452885
1.683716
1.473675
2.345932
1.683362
2.346877
1.474560
-0.753177
-1.808001
-0.891655
-2.608059
b
0.650343
1.726044
-0.074816
-1.022121
0.581808
0.036968
0.724213
-0.881056
-0.072331
0.778661
-1.269858
0.235118
c
0.021147
0.052516
0.745077
1.218132
1.289096
-0.747865
-1.250935
-1.275993
-0.001568
0.021870
-0.036844
0.004902
Krait-|a|
0.527(12)
Krait-|b|
0.645(15)
Krait-|c|
0.050(1)
1.678(26)
0.0430(7)
0.747(12)
1.678(26)
0.0430(7)
0.747(12)
0.75(30)
0.011(4)
0.023(9)
2.598(27)
0.209(2)
0.0654(7)
4.1.6 DISCUSSION
The rotational spectrum for CPCA has been extended to the 5-15 GHz regime,
with the new high resolution measurements taken using a PBFT microwave
spectrometer. The experimental rotational transitions are shown in Tables 4.1.1 and
4.1.2 and the rotational constants obtained from this study. Measurements were
extended for the low energy conformer of CPCA to include all of the singly substituted
13
C and singly substituted -OD positions. To perform the fit on the measured transitions
62
for each of the isotopologues, the centrifugal distortion constants were held fixed to the
values obtained in the study by Marstokk et al. This was done due to these centrifugal
distortion constants being more accurately fit than the distortion constants obtained in
this study because of the measurement of large J and K transitions. By measuring
rotational transitions with larger J and K values, the distortion with respect to each of
these quantum numbers can be more accurately fit, compared to the fit that was limited
to low J transitions. A Kraitchman analysis was performed on this CPCA conformer and
these Kraitchman coordinates, along with the best fit structure coordinates, are shown
in Table 4.1.7. The substituted coordinates from the Kraitchman analysis seem to agree
fairly well with the best fit structure obtained from the nonlinear least squares fit. Tables
4.1.8 and 4.1.9 show the key molecular structure parameters of the bond lengths and
angles of the B3LYP/aug-cc-pVQZ calculated values compared to the parameters that
were obtained during the structure fit.
Table 4.1.8 Bond lengths obtained from the structure fit of CPCA (Å). Unreported
bond lengths were fixed at calculated B3LYP/aug-cc-pVQZ values.
Interatomic Distance Microwave Fit Value
(Å)
r(C1-C3)
1.548
r(C1-C6)
1.521
r(C1-C9)
1.467
r(C3-C6)
1.497
63
Calculated
Value (Å)
1.517
1.517
1.478
1.486
Table 4.1.9 Angles obtained from the structure fit of CPCA (°). The last 2 listed angles
are dihedral angles, indicating the non-planarity of carbon atoms 3 and 6. Unreported
angles were held fixed to calculated B3LYP/aug-cc-pVQZ values.
Angle
<(C3-C1-C6)
<(C6-C3-C1)
<(C1-C6-C3)
<(C1-C9-O10)
<(C1-C9-O11)
<(C3-C1-C9-O10)
<(C6-C1-C9-O10)
Microwave Fit
Value(°)
58
60
62
112
126
148
-146
Calculated
Value(°)
59
61
61
112
126
146
-146
It can be seen that the cyclopropane ring does not have equal C1 – C3 and C1 –
C6 bond lengths as the B3LYP/aug-cc-pVQZ calculation predicted. The greatest change
in bond length compared to the calculated value was the C1-C3 bond changing by ~0.03
Å. The bond angles in the ring remained fairly constant, with the angles changing by
only 1°. The bond lengths within the cyclopropane ring also agree fairly well with
previous structural work. Differences between these structures most likely arise from the
combination of the microwave data with electron diffraction work as molecules may
have slightly different structures in the gas phase.
After searching for transitions corresponding to the higher energy conformer with
the geometry shown in Figure 4.1.1 (bottom) of CPCA, 10 weak rotational transitions
were measured and definitively assigned to be from this conformer. The experimentally
fit rotational constants agreed within 1% of the rotational constants obtained from the
B3LYP calculations and <1% with previous calculations. The intensities of the measured
transitions of this high energy conformer seemed to reflect the abundances of the two
conformers somewhat that was calculated under equilibrium conditions at room
64
temperature, 85% and 15%. However it seemed the abundance was lower for the high
energy conformer in the gas phase under the experimental conditions. The intensities of
the 000 to 101 transitions for each of the conformers can be observed in Figure 4.1.2
taken after the same number of pulsed beam cycles. The high energy conformer was
similar to the 13C signals of the low energy conformer, representing 1% natural
abundance, so from this comparison we concluded the abundance of this high energy
conformer in the gas phase was ~ 1%.
Figure 4.1.2 Example transitions of the low energy conformer (left) and higher energy
conformer (right) taken of the 000 to 101 transition. Both transitions were recorded after
~230 pulsed-beam cycles.
65
4.2 1,2-CYCLOHEXANEDIONE
4.2.1 INTRODUCTION
The important organic compound 1,2-cyclohexanedione (CDO) is widely used in
organic syntheses and has many industrial applications. It can be prepared by a number
of different reactions. One method of CDO preparation is by the ring-opening of
epoxides, which are versatile organic intermediates, easily prepared from olefins or
carbonyl compounds using Bi catalysts.22,23 It can also undergo many organic reactions,
including a Michael addition of CDO to β-nitrosytrenes.24 It is also added to a number of
different consumer products to alter the scent and flavor, such as food products,
perfumes, and tobacco products.25,26 CDO has gained attention in biological chemistry,
as it was found to selectively and reversibly modify arginine residues in proteins at the
guanidino group,27 allowing for primary protein sequences to be determined.28
CDO is a solid at room temperature and melts at about 35 °C into a yellow liquid.
The vapor pressure was sufficiently high at 35 °C that strong signals of the parent
isotopologue could be obtained by pulsed-beam Fourier transform (PBFT) microwave
spectroscopy. CDO can exist in either the diketo or monoenol forms,29 but in the gas
phase it is mostly monoenolic (Figure 4.2.1). Searches for rotational transitions for the
diketo form were not successful. The gas phase structure of the monoenolic form of
CDO has been previously determined using electron diffraction methods.30 Since there
are limitations (in the sense that the structures are distorted) to electron diffraction data,
it is beneficial to measure microwave data also for this molecule. Infrared spectroscopy
and quantum chemistry computations for CDO were reported by Chakraborty et al.31
66
Figure 4.2.1 The best fit structure of 1,2-cyclohexanedione (enol tautomer) showing the
best fit bond lengths (Å) and the bond angles (degrees) for the cyclohexane ring. The
C3-C5-C2 bond angle passes over the C5-H16 bond. All C-H bond lengths are 1.09(1)
Å.
4.2.2 MICROWAVE MEASUREMENTS
The microwave spectrum was measured for the parent isotopologue, all singly
substituted 13C isotopologues (under natural abundance), and a deuterium substituted
isotopologue at H9 in the 4-14 GHz region using a PBFT-type spectrometer described in
chapter two. There were 72 transitions measured in total, 16 for the parent
isotopologue, 14 for the deuterium substitution at H9, and 7 for each single substituted
13
C isotopologue. The numbering scheme used in the analysis is given in Figure 4.2.1.
The sample was purchased from Sigma Aldrich (97%) and was used without
further purification. It was loaded into a glass sample cell and attached to a pulsed valve
(General Valve series 9). The sample cell and valve were heated to ~35 °C to obtain
67
sufficient vapor pressure of the sample in the neon gas stream. The pressure inside the
spectrometer was maintained at 10-6 to 10-7 Torr prior to the pulsed injection of the
gaseous molecular sample and the Ne carrier gas. The Ne backing pressure was
maintained at ~1 atm during the microwave measurements. The signal strength was
sufficiently strong that the singly substituted 13C isotopologue transitions were measured
under the same conditions in 100 beam pulse cycles under natural abundance of 13C.
A deuterated sample of 1,2-cyclohexanedione was prepared by mixing equimolar
amounts of 1,2-cyclohexanedione (Sigma Aldrich, 97%) and CH3OD (Cambridge
Isotope Laboratories, Inc., 99%) overnight. The remaining CH3OH was removed under
reduced pressure and the deuterated 1,2-cyclohexanedione was crystallized and
transferred to a small vial. Similar instrumental conditions were used to measure the
deuterated transitions. All measured transitions are shown in Tables 4.2.1-3.
Table 4.2.1 Results of the measurements and least squares fit calculations for CDO
parent isotopologue transitions. The standard deviation of the fit is 0.002 MHz.
Frequencies are given in MHz.
J′Ka’ Kc’
111
202
212
221
202
212
211
303
211
221
220
321
221
J″Ka” Kc”
000
111
111
202
101
101
110
202
101
110
110
220
111
obs
o-c
4482.397
5484.907
6063.935
6101.431
6544.965
7123.990
7625.426
9277.312
9466.226
10805.592
11105.305
11256.720
11586.341
-0.001
0.000
0.001
0.001
0.001
-0.001
0.002
-0.001
0.000
0.000
-0.002
0.000
0.005
68
404
220
312
303
111
202
11850.350
11886.047
14118.823
0.000
-0.004
0.000
Table 4.2.2 Results of the measurements and least squares fit calculations for D-CDO
isotopologue transitions. The standard deviation of the fit is 0.005 MHz. Frequencies are
given in MHz.
J′Ka’ Kc’
202
212
202
212
413
211
303
313
303
313
322
312
321
404
J″Ka” Kc”
111
111
101
101
404
110
212
212
202
202
221
211
220
303
obs
o-c
5318.014
5948.716
6426.843
7057.545
7169.658
7448.654
8504.260
8775.248
9134.961
9405.953
10048.019
10958.520
10961.087
11672.237
0.002
-0.002
0.000
-0.003
0.005
0.001
0.008
-0.003
0.004
-0.003
-0.007
0.000
-0.008
0.007
69
13
J′Ka’ Kc’
212
202
211
313
303
414
404
J″Ka” Kc”
13
C1
obs
13
C2
 o-c
obs
 o-c
13
C3
obs
 o-c
13
C4
obs
 o-c
13
C5
obs
 o-c
C6
obs
 o-c
111 6037.642 -0.001 6031.021
0.000 5990.835 0.000 6051.833 0.000
5991.664 -0.001 6051.919
0.002
101 6513.195 0.002 6506.678 -0.002 6468.898 0.001 6531.595 0.000
6469.952 0.001 6531.386
0.003
110 7611.114 -0.001 7598.334
0.000 7520.632 0.000 7612.600 0.000
7515.111 0.000 7614.246 -0.001
212 8888.752 0.003 8880.426
0.001 8830.809 -0.001 8915.280 0.002
8833.774 -0.001 8914.873 -0.001
202 9218.580 -0.001 9212.411
0.001 9179.673 0.000 9256.690 -0.005
9185.286 -0.001 9255.227 -0.001
313 11628.328 -0.002 11618.853 -0.001 11563.428 0.001 11668.618 0.005 11569.157 0.001 11667.542
0.000
303 11773.636 0.001 11766.207
0.000 11726.815 -0.001 11823.708 -0.003 11735.216 0.000 11821.705
0.000
13
Table 4.2.3 Results of the measurements and least squares fit calculations for C isotopologues of 1,2-CDO. The standard deviation
of each of the fits (in order of numbering in Figure 1) are 0.002 MHz, 0.001 MHz, 0.001 MHz, 0.004 MHz, 0.001 MHz, and 0.002 MHz.
Frequencies are given in MHz.
70
4.2.3 CALCULATIONS
Ab initio calculations were performed to obtain initial values of rotational
constants for 1,2-cyclohexanedione using the Gaussian 09 suite with MP2/6-311++G**.
The calculations predicted the lowest energy structure to be the enol tautomer. This was
determined to be true, due to the intense signals observed for the rotational transitions
corresponding with the enol structure, as well as the strong signals observed with each
of the singly substituted 13C isotopologues. Predicted transitions were not observable for
the diketo structure after significantly searching. Comparisons of the structural
parameters with those determined from the least squares structure fit are given in
Tables 4.2.4 and 4.2.5.
Table 4.2.4 Bond distances obtained from the fit. Bond lengths are in Å. Starred bond
lengths(*) were fixed at calculated (Gaussian) values.
Interatomic Distance Microwave Fit Value
(Å)
r(C1-C4)
1.368
r(C1-C3)
1.502
r(C3-C5)
1.530*
r(C5-C2)
1.534
r(C2-C6)
1.510
r(C6-C4)
1.479
r(C6-O7)
1.229*
r(C4-O8)
1.356*
r(C1-H10)
1.088*
r(C3-H13)
1.096*
r(C3-H14)
1.101*
r(C5-H15)
1.097*
r(C5-H16)
1.095*
r(C2-H11)
1.100*
r(C2-H12)
1.094*
r(O8-H9)
0.971*
71
Calculated
Value (Å)
1.353
1.505
1.530
1.530
1.509
1.485
1.229
1.356
1.088
1.096
1.101
1.097
1.095
1.100
1.094
0.971
Table 4.2.5 Angles obtained by fitting the experimental and rotational constants for
eight isotopologues. Angles are listed in degrees. The last 2 listed angles are dihedral
angles, indicating the non-planarity of the cyclohexane skeleton.
Angle
Microwave Fit
Value(°)
121
112
110
110
117
121
53
-17
<(C4-C1-C3)
<(C1-C3-C5)
<(C3-C5-C2)
<(C5-C2-C6)
<(C2-C6-C4)
<(C6-C4-C1)
<( C1-C3-C5-C2)
<(C1-C4-C6-C2)
Calculated
Value(°)
122
111
110
111
117
122
4.2.4 ROTATIONAL CONSTANTS
The experimental rotational and centrifugal distortion constants for the parent
isotopologue were determined using a least squares fitting program, FITSPEC32, and
are given in Table 4.2.6.
Table 4.2.6 MEASURED rotational constants and the “best fit” CALCULATED values
for rotational constants obtained from the structure fit, given in MHz. The centrifugal
distortional constants (DJ and DK) were obtained from the microwave fit of the parent
isotopolgue and are DJ=0.04355 KHz and DK=0.4358 KHz. The distortion constants
were held fixed to these values when obtaining the microwave fit for each of the other
isotopologues. The standard deviation for the structure fit is 0.18 MHz.
ISOTOPOLOGUE
Parent
A
B
MEASURED
3161.6006(12)
2101.5426(3)
72
CALCULATED
3161.7844
2101.6104
(M. – C.)
-0.1838
-0.0678
DCDO
13
C1
13
C2
13
C3
13
C4
13
C5
13
C6
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
1320.7976(4)
3158.4864(27)
2049.6554(5)
1299.6880(3)
3120.0650(59)
2099.4632(7)
1312.7269(4)
3122.1020(33)
2095.4979(4)
1311.8413(2)
3147.0237(31)
2071.3833(3)
1306.4843(2)
3152.2477(119)
2098.2463(13)
1317.8627(7)
3152.8131(30)
2069.2089(3)
1307.4857(2)
3149.7990(51)
2098.8533(6)
1317.6887(3)
1320.8582
3158.0533
2049.6654
1299.5564
3119.8658
2099.4394
1312.6387
3122.1785
2095.3309
1311.9275
3147.2021
2071.4420
1306.5140
3152.1881
2098.0731
1317.8290
3152.9266
2069.3500
1307.5010
3149.9345
2098.9441
1317.7380
-0.0606
0.4331
-0.0100
0.1316
0.1992
0.0238
0.0882
-0.0765
0.1670
-0.0862
-0.1785
-0.0586
-0.0296
0.0596
0.1731
0.0337
-0.1135
-0.1411
-0.0153
-0.1355
-0.0908
-0.0493
Similar analyses were carried out for all singly substituted isotopologues, but the
centrifugal distortion constants were held fixed to the values obtained from the parent
isotopologue for each fit. The deviations (o-c) between the best fit calculated (c) and
observed (o) frequencies are listed in Tables 4.2.1-3. The J and K values for reported
transitions ranged from 0 to 4 and this range is believed to be sufficient to obtain fair
values for the distortion constants. Higher J-values could be obtained to refine the
parameters, but signal strength would be lower.
4.2.5 MOLECULAR STRUCTURE
The rotational constants obtained for each isotopologue from fitting the measured
rotational transitions were used in a nonlinear least squares fit program to determine the
73
best fit coordinates of the atoms in 1,2-cyclohexanedione relative to the parent
isotopologue’s center of mass. During the least squares fit, all hydrogen atom
coordinates were held fixed relative to the atom it was bonded to, as was determined
from the Gaussian 09 calculation. The coordinates of atoms C1, C6, and O7 were also
held constant. The carbon atoms at positions 3 and 5 were varied using the same
variable parameters as well as the group with atoms C4, O8, and H9. With these
constraints, only 9 variable parameters remained and were precisely determined from
the least squared structure fitting analysis. The variable parameters were the a, b, and c
Cartesian coordinates in the principal axes system for C2, C3 and C5, and C4.
Table 4.2.7 Atom Cartesian coordinates in a, b, c system for the best fit structure of
CDO, and the Kraitchman determined values (Krait.).
Atom
C1
C2
C3
C4
C5
C6
O7
O8
H9
H10
H11
H12
H13
H14
H15
H16
a
0.4778
0.7998
1.8673
-0.6310
1.9001
-0.5477
-1.5905
-1.8784
-2.4687
0.3583
0.9674
0.7767
2.5752
2.2008
1.7254
2.8826
b
1.4682
-1.4119
0.8779
0.6956
-0.5610
-0.7772
-1.4249
1.2095
0.4386
2.5496
-1.4238
-2.4494
1.4986
0.8976
-0.5529
-1.0125
c
-0.1001
-0.2573
-0.1244
-0.0366
0.3943
-0.0307
0.0310
0.1026
0.0942
-0.0755
-1.3445
0.0880
0.4362
-1.1734
1.4772
0.2208
|a| -Krait.
0.476(3)
0.793(2)
1.8613(8)
0.615(2)
1.8996(8)
0.553(3)
|b| -Krait.
1.462(1)
1.413(1)
0.866(2)
0.692(2)
0.553(3)
0.776(2)
|c| -Krait.
0.083(18)
0.230(7)
0.160(9)
0.01*i(25)
0.397(4)
0.047(32)
2.4653(6)
0.392(4)
0.126(12)
The experimental A, B, and C rotational constants and the deviations of the “best
fit” calculated values from the experimental values are listed in Table 4.2.6. Values of
74
the atomic coordinates obtained in the structural fit are listed in Table 4.2.7. Coordinates
for the substituted atoms were also obtained by performing Kraitchman analyses, using
the Kiesel KRA program, and these values are also shown in Table 4.2.7. Agreement
between the structural fit values and Kraitchman values is very good, with the exception
of several of the c-coordinates as these substituted atoms lie close to the principal axis
and are not as reliable.
4.2.6 DISCUSSION
The rotational spectrum of 1,2-cyclohexandione has been measured using PBFT
microwave spectroscopy and all of the measured lines were assigned. The
experimental rotational transitions of all the isotopologues are listed in Tables 4.2.1-3,
as well as the best fit structural parameters given in Tables 4.2.4 and 4.2.5. The best fit
structure obtained from microwave data (Figure 4.2.1) is in good agreement with the
structure obtained from the electron diffraction data. The C-C bond lengths also agreed
well with values calculated from Gaussian 09. An exception is the C1-C4 bond length
which was 0.025 Å larger than the calculated value. The dihedral angles for the best fit
structure are <( C1-C3-C5-C2) = 53° and <(C1-C4-C6-C2) = -17°, an indication of the nonplanarity of the molecule. Carbon atoms C1, C2, C3, C4, and C6 are all nearly in the
same plane, with only C5 being significantly out of plane. A more distorted structure
was found for 1,2-cyclohexanedione by Hedberg, et, al.33 using electron diffraction. That
structure exhibited a mixture of a chair form of C2h symmetry and a twisted boat form of
D2 symmetry which will account for the differences in the present microwave structure.
Obtaining more accurate microwave values for the 1,2-cyclohexandione bond lengths
75
and angles would require measurements of significantly more rotational transitions for
additional substituted isotopologues.
76
5. MICROWAVE MEASUREMENTS ON MOLECULES WITH ELECTRIC
QUADRUPOLE INTERACTIONS
Electric quadrupole interactions between the quadrupole moments of nuclei and
the electric field gradients within molecules adds to the complexity of the observed
microwave spectra, yielding a very rich spectra full of rotational transitions. The analysis
of the rich spectra yields important information about the electronic structure of the
molecule which may lead to some insight into bonding and chemical reactivity. This
chapter focuses on the molecules maleimide, a related molecule phthalimide, and
4a,8a-azaboranaphthalene. The quadrupole coupling strengths were determined for the
quadrupolar nuclei in each system yielding important electronic structure information
about these molecules in addition to the molecular structure parameters that are
typically obtained from these microwave studies. In the case of 4a,8aazaboranaphthalene, the aromatic character was determined from an extended
Townes-Dailey analysis which will be described in more detail in the respective section.
This analysis allows for the determination of the electron occupancies in the valence
hybridized orbitals in each of the quadrupolar nuclei, 11B and 14N.
Microwave spectroscopy is a valuable tool to determine the electric quadrupole
coupling strengths in molecules due to the low rotational states that are able to be
probed with extremely high resolution. The determination of the electric quadrupole
coupling strengths is an important parameter to identify different isomers present of a
molecule34 or even a different but related structure,35 as well as characterizing the ionic
character36 in some systems. This chapter details the experiment and the results
obtained for maleimide, phthalimide, and 4a,8a-azaboranaphthalene.
77
5.1 MALEIMIDE
5.1.1 INTRODUCTION
Maleimide (Mal) and its derivatives are important compounds in biological
chemistry and in other types of applications, such as in biotechnology and organic
synthesis. Fluorescent Mal derivatives are used to study the in vivo processes of
intracellular trafficking, membrane association, and auto toxicity.37,38 These Mal
compounds are also the backbone of some enzyme inhibitors.39 In organic synthesis,
Mal and its derivatives play an important role in the protection of amino groups.40
Bismaleimide resins are important in industrial applications due to the high temperature
performance, toughness, and low cost in products such as tires.41,42,43 Polyethylene
glycol (PEG)-Mal compounds are often used to attach proteins to surfaces or PEG to
different amino acid residues.44,45 Synthesis of Mal is achieved with copolymers of
styrene and maleic anhydride while reacting with gaseous NH3 at elevated
temperatures under low pressure environments.46 Mal can also be prepared from
dimethyl maleate through the Rinkes method.47
Maleimide or 2,5-pyrroledione (IUPAC), has a slight yellow crystalline
appearance. The melting point of Mal is 92-95 °C48 and the vapor pressure at 70 ºC is
sufficient to measure the pure rotational spectrum by pulsed-beam microwave
spectroscopy. Mal has been studied by X-ray diffraction49, electron diffraction50, and IR
spectroscopic techniques. In order to obtain accurate gas phase structural parameters
of Mal, the rotational spectrum should be measured for this molecule. This study
extends the structural parameters of Mal to include these gas phase microwave
measurements, which are important as structures may be distorted in solid phases
78
when compared to structural parameters obtained in the gas phase from microwave
studies.
5.1.2 MICROWAVE MEASUREMENTS
The Mal sample was purchased from Sigma Aldrich (99%) and was used without
further purification. All measurements were made in the 5 – 12 GHz range using a
Flygare-Balle type pulsed-beam Fourier transform microwave spectrometer that has
been previously described. The measured rotational transitions for the parent are listed
in Table 5.1.1.
Table 5.1.1 Measured rotational transitions of the parent isotopologue of Maleimide,
shown in MHz.
J′ Ka’ Kc’ F’
1 1 0 1
1 1 0 1
1 1 0 2
1 1 0 1
1 1 0 2
1 1 0 0
2 1 1 2
2 1 1 2
2 1 1 3
2 1 1 1
3 1 2 3
3 1 2 4
3 1 2 2
3 1 2 3
3 1 2 3
3 1 2 4
3 1 2 2
3 0 3 2
3 0 3 3
3 0 3 4
3 0 3 2
J″ Ka” Kc” F”
1 0 1 1
1 0 1 2
1 0 1 1
1 0 1 0
1 0 1 2
1 0 1 1
2 0 2 2
2 0 2 3
2 0 2 3
2 0 2 1
3 0 3 3
3 0 3 3
3 0 3 3
3 0 3 4
3 0 3 2
3 0 3 4
3 0 3 2
2 1 2 2
2 1 2 2
2 1 2 3
2 1 2 1
79
obs
o-c
5059.705
5060.191
5060.769
5060.917
5061.257
5062.367
5725.561
5726.190
5726.808
5727.498
6827.303
6827.774
6827.938
6828.111
6828.403
6828.586
6829.038
8214.566
8215.661
8215.991
8216.337
-0.002
-0.000
-0.001
-0.001
0.002
0.003
0.003
0.005
0.003
-0.001
0.002
0.004
0.002
-0.002
0.005
0.003
0.005
0.003
0.000
0.005
0.002
3
4
4
4
1
1
1
5
5
4
4
4
4
4
4
0
1
1
1
1
1
1
2
2
0
0
0
2
2
2
3
3
3
3
1
1
1
3
3
4
4
4
2
2
2
3
4
5
3
0
2
1
5
6
4
5
3
3
5
4
2
4
4
4
0
0
0
5
5
3
3
3
4
4
4
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
2
4
4
4
0
0
0
4
4
3
3
3
3
3
3
3
4
5
3
1
1
1
5
6
3
4
2
3
5
4
8216.799
8466.040
8467.432
8467.795
8568.683
8569.553
8570.125
11862.727
11862.762
12726.967
12727.283
12727.493
12191.258
12191.292
12191.410
-0.001
-0.005
-0.007
-0.002
-0.004
-0.001
-0.007
0.002
-0.004
-0.002
-0.003
0.001
0.004
0.005
-0.007
Prior to the pulse of the molecular beam, the pressure inside the vacuum cavity
was maintained at 10-6 to 10-7 Torr. Ne was used as the carrier gas and the backing
pressure was maintained at ~1 atm. In order to obtain sufficient vapor pressure of the
solid Mal sample, the pulsed valve and sample cell were heated to ~70 °C as this
temperature provided a strong parent test signal that can be seen in one pulsed beam
cycle. The 13C isotopologues were measured under natural abundance, using the same
method as was used to measure the parent transitions. A –ND isotopologue sample
was prepared and its transitions were also measured. The –ND isotopologue was
prepared by dissolving equimolar amounts of both Mal and D2O and allowing to mix and
exchange H for D over several days. Most of the remaining water was removed under
reduced pressure by pumping on the –ND sample for several hours at ~ 30 °C. All of
the isotopologue transitions are listed in Table 5.1.2. The labeling scheme for each of
the substituted atoms can be seen in the best fit structure, shown in Figure 5.1.1. There
was a small amount of line broadening observed for the –ND isotopologue transitions.
80
This is most likely caused by the D quadrupole coupling, but there was no attempt to
assign the D quadrupole splitting as these hyperfine splittings were not resolved.
Figure 5.1.1 Best fit structure of Maleimide showing the fit bond lengths (Å) and angles
(°). The bond lengths and angles are equivalent on the corresponding side across the
symmetry axis.
Table 5.1.2 Measured rotational transitions of each unique 13C isotopologue and the –
ND isotopologue, shown in MHz.
Rotational Transitions
J′ Ka’ Kc’ F’
J″ Ka” Kc” F”
1 1 0 1
1 0 1 1
1 1 0 1
1 0 1 2
1 1 0 2
1 0 1 1
1 1 0 1
1 0 1 0
1 1 0 2
1 0 1 2
1 1 0 0
1 0 1 1
13
obs
5066.350
5066.836
5067.408
5067.557
5067.899
5069.015
C1&4
C2&3
 o-c
obs
-0.001
0.003
-0.006
-0.000
0.002
0.005
4925.181
4925.664
4926.245
0.004
-0.001
0.000
4926.732
-0.000
81
13
 o-c
obs
-ND
 o-c
2
2
2
3
3
3
3
1
1
1
3
3
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
3
3
2
2
2
2
2
2
1
2
4
3
2
0
2
1
3
2
1
3
2
2
2
2
2
3
3
3
3
0
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
3
3
3
3
0
0
0
2
2
1
1
1
1
2
3
1
3
3
2
2
1
1
1
2
1
1
2
1
2
5456.652
5457.303
5458.627
6813.879
6814.322
-0.002
0.006
-0.004
0.004
6725.419
-0.006
6726.713
8408.939
8409.807
8410.388
0.006
-0.001 8225.167
-0.003 8226.051
-0.002 8226.633
8451.905
8452.558
11689.513
0.005 11690.633
0.001 11691.298
-0.004 11691.790
-0.004
8559.294
8560.161
8560.735
0.002
-0.002
-0.008
12051.583
12052.704
-0.001
0.005
11893.164
11893.816
11894.299
-0.002
0.003
-0.001
-0.003
0.003
0.002
-0.004
-0.001
0.004
5.1.3 CALCULATIONS
Ab initio calculations were performed to predict the structure of Mal using the
Gaussian 09 suite, on the HPC system at the University of Arizona. The calculations
were performed using an MP2 method with the 6-311++G** basis set. The Gaussian
calculated rotational and quadrupole coupling constants were used in Pickett’s SPCAT
program to predict the b-type rotational transitions expected to be observed, as the
calculated Gaussian structure had a large b-dipole of ~1.6 D. To predict the
isotopologue rotational constants, a set of scale factors – the ratios between the
experimental rotational constants of the parent and their corresponded ab initio values,
were used to provide reasonable predictions. From the ab initio parent isotopologue
molecular structure, the mass of the substituted atom was changed and the moments of
inertia and corresponding rotational constants were recalculated using Kisiel’s PMIFST
program. These calculated rotational constants were multiplied by the scale factors
obtained from the parent to obtain corrected rotational constants for each of the singly
82
substituted isotopologues. These scaled rotational constants were used in the SPCAT
program, along with the experimentally determined quadrupole coupling constants of
the parent, to predict the isotopologue rotational transitions. The experimental results
agreed with those scaled values very well, within 1%.
5.1.4 ROTATIONAL CONSTANTS
The rotational constants, quadrupole coupling constants and centrifugal distortion
constants were all determined from the measured rotational transitions using Pickett’s
SPFIT program and all the fit values are shown in Table 5.1.3. During the fits of the
isotopologue rotational and quadrupole coupling constants, the centrifugal distortion
constants were held fixed to what was obtained from the parent. The rotational
constants obtained from the best fit gas phase structure are shown with the
experimentally fit values, along with their differences (M – C) in Table 5.1.4. The
calculated rotational constants from the best fit structure had a standard deviation of
0.285 MHz from the experimental values.
Table 5.1.3 Fit and calculated spectroscopic constants of the isotopologues.
Parent
A/MHz 6815.3251(12)
B/MHz 2361.85011(64)
C/MHZ 1754.32750(64)
0.232(24)
DJ/kHz
DJK/kHz
0.546(54)
1.5χaa/MHz
2.4227(53)
1.3679(15)
0.25(χbbχcc)/MHz
N
36
σ/kHz
3
MP2/6- B3LYP/aug13
13
311++G**
cc-pVTZ
C(1&4)
C(2&3)
-ND
6818.4054
6848.9871 6813.9509(16) 6668.1911(18) 6493.8111(13)
2340.2953
2364.7515 2347.6975(18) 2356.7728(19) 2361.90584(80)
1742.2867
1757.8263 1746.3107(10) 1741.7171(10) 1732.33683(56)
0.232*
0.232*
0.232*
0.546*
0.546*
0.546*
2.4996
2.4968
2.4130(87)
2.437(12)
2.436(11)
1.4520
1.4156
1.3702(30)
1.3731(32)
1.3826(24)
13
4
* Centrifugal distortion constants were held fixed to the parent during fits of 13C isotopologues
83
12
3
12
3
Table 5.1.4 Measured rotational constants compared to the rotational constants
calculated of the best fit structure, also showing the difference (M – C), shown in MHz.
The standard deviation of the best fit structure was 0.285 MHz.
ISOTOPOLOGUE
Parent
A
B
C
13
C1
A
B
C
13
C4
A
B
C
13
C2
A
B
C
13
C3
A
B
C
-ND
A
B
C
MEASURED
6815.3251
2361.8501
1754.3275
6813.9509
2347.6975
1746.3107
6813.9509
2347.6975
1746.3107
6668.1911
2356.7728
1741.7171
6668.1911
2356.7728
1741.7171
6493.8111
2361.9058
1732.3368
CALCULATED
6815.8202
2362.1247
1754.1855
6814.1430
2347.7251
1746.1215
6814.1430
2347.7251
1746.1215
6667.8319
2356.9009
1741.3722
6667.8319
2356.9009
1741.3722
6493.7284
2362.1247
1732.0744
(M – C)
-0.4951
-0.2746
0.1420
-0.1921
-0.0276
0.1892
-0.1921
-0.0276
0.1892
0.3592
-0.1281
0.3449
0.3592
-0.1281
0.3449
0.0827
-0.2189
0.2624
5.1.5 MOLECULAR STRUCTURE
A best fit gas phase structure, which is an averaged structure of both equilibrium
and ground state coordinates, was obtained for Mal using a nonlinear least squares
fitting program with the measured rotational constants from each of the isotopologues.
The fitting program varies the Cartesian coordinates of the atoms within the molecule
and a “best fit” structure is determined. This best fit structure yields calculated moments
of inertia closest to the experimentally obtained values (smallest deviations). From the
MP2 calculation, the structure was predicted to be planar with C2v symmetry. The
inertial defect calculated using the experimental parent rotational constants was ∆ = 0.0536 amu Å2, confirming that the actual structure of Mal is indeed planar with a value
84
very close to zero. The slight negative value of the inertial defect indicates Mal exhibits
out of plane vibrations.51 The Kraitchman determined c-coordinates of H6 are small
(Table 5.1.5) further supporting a planar structure of Mal, and indicating no large
amplitude motions of H6.
In the structure fit, there were a total of 4 varied parameters representing the
movement of the carbon atoms in the a-b plane. With the Mal structure being planar, all
c-coordinates were set to zero. Assuming that the C2v symmetry is maintained, the
varied parameters in the fit were the same for corresponding atoms on each side of the
line of symmetry, with the exception of the varied parameters in the a-direction which
were opposite for each corresponding atom. The only fixed atoms in the fit were the N
and H atoms forming the imide group, so the N-H bond length was fixed to the
calculated equilibrium value. The H and O atoms bonded to the C atoms in the ring
were varied by the same parameters as the carbon atom it is bonded to, resulting in the
C-H and C=O bond lengths to be fixed to calculated equilibrium values. With these
constraints and varied parameters, the standard deviation of this nonlinear least
squares structure fit was 0.285 MHz.
A Kraitchman analysis was also performed on all isotopically substituted atoms
using the Kisiel KRA program. The best fit structure coordinates as well as the
Kraitchman determined coordinates for each substituted atom is shown in Table 5.1.5.
The coordinates from the best fit structure and Kraitchman analysis seem to agree very
well with the exception of the a-coordinate of H6, shown as an imaginary number. This
substituted atom lies on the b-axis, thus making the Kraitchman determined coordinate
unreliable.
85
Table 5.1.5 Principle a and b coordinates (Å) of the best fit structure compared to the
coordinates of the unique singly substituted 13C substituted and –ND isotopologues
determined from a Kraitchman analysis. The Kraitchman coordinates only show the
magnitude of the substituted coordinates.
Atom
C1
C2
C3
C4
N5
H6
H7
H8
O9
O10
a
1.1452
0.6820
-0.6820
-1.1452
0.0000
0.0000
1.3659
-1.3659
-2.2886
2.2886
b
-0.1362
1.2894
1.2894
-0.1362
-0.9108
-1.9216
2.1285
2.1285
-0.5401
-0.5401
Krait-|a|
1.1474(13)
0.6689(23)
0.6689(23)
1.1474(13)
Krait-|b|
0.123(12)
1.2856(12)
1.2856(12)
0.123(12)
0.119*i(13)
1.91988(78)
The structural parameters obtained from the nonlinear least squares fit and the
Gaussian calculation are shown in Tables 5.1.6 (bond lengths) and 5.1.7 (angles).
Figure 5.1.1 shows the structural parameters obtained from the structure fit. Because
Mal has C2v symmetry, only half of the bond lengths and angles are shown in the figure
because these values are exactly equal on the corresponding side across the symmetry
axis. The double C2 – C3 bond increased by 0.044 Å from the calculation whereas the
single bonds decreased by 0.002 Å from the calculated values. Most angles changed by
1° in the fit from the calculation with the exception of three of the angles that had the
same values as in the calculation.
86
Table 5.1.6 Microwave fit values for bond lengths (in angstroms) compared to MP2/6311++G** calculated values. Corresponding bond lengths across line of symmetry are
equal.
Interatomic Distance Microwave Fit Value
(Å)
r(C2-C3)
1.364
r(C3-H8)
1.082*
r(C3-C4)
1.499
r(C4-O9)
1.213*
r(C4-N5)
1.383
r(N4-H6)
1.011*
Calculated
Value (Å)
1.345
1.082
1.502
1.213
1.396
1.011
*Values were fixed to Gaussian calculated equilibrium values
Table 5.1.7 Microwave fit values for angles (in degrees) compared to MP2/6311++G** calculated values. Corresponding angles across line of symmetry are equal.
Angle
<(H7-C2-C3)
<(H7-C2-C1)
<(C1-C2-C3)
<(C2-C1-O10)
<(C2-C1-N5)
<(O10-C1-N5)
<(C1-N5-C4)
<(C1-N5-H6)
Microwave Fit Value
129
123
108
127
106
126
112
124
Calculated
129
122
109
128
105
127
112
124
5.1.6 DISCUSSION
The pure rotational spectrum of Mal was measured in the 5-12 GHz range using
a Flygare-Balle type microwave spectrometer and all measured transitions were
assigned for the first time, providing experimentally determined rotational, centrifugal
distortion, and quadrupole coupling constants. Two unique singly substituted 13C
isotopologues and an –ND isotopologue were also measured and the respective
87
rotational and quadrupole coupling constants were determined. The nonlinear least
squares structure fit performed with the rotational constants of all the measured
isotopologues had a standard deviation of 0.285 MHz, providing the first gas phase
structure of this molecule with high accuracy. The best-fit experimental bond lengths
were close (~0.01 Å) to values from the Gaussian calculations. The greatest difference
in bond length being the C2 – C3 bond (~0.04 Å different). The best-fit experimental
bond angles deviated by 1° from the Gaussian calculations. These differences between
the experiment and the calculations are most likely caused from the calculated
structures being an equilibrium structure whereas the experimental structure is a
vibrationally averaged ground state structure.
The structure obtained from the electron diffraction study was similar to the
structure obtained in the present work. The largest differences between the current
microwave and previous electron diffraction structures were seen in the bonds of C2 –
C3 and C4 – N5, which deviated by 0.03 and 0.02 Å. The C2 – C3 bond is larger and
the C4 – N5 bond is smaller than in the electron diffraction study. To obtain a more
complete and accurate gas phase structure and fit the remaining bond lengths and
angles, a unique single D substitution at H7, a unique 18O single substitution and 15N
isotopologues will need to be measured. Even though the structure determined for Mal
is an averaged structure made up from both equilibrium (re) and ground (r0) state atomic
coordinates of the different isotopologues, these differences are small and so the
determined structure is an excellent representation of the vibrationally averaged ground
state.
88
5.2 PHTHALIMIDE
5.2.1 INTRODUCTION
Phthalimide (PhI) and its derivatives are important compounds widely utilized in
industry as well as in medicinal chemistry, due to the biological activity of PhI and its
derivatives. Derivatives of PhI have been used in medicinal chemistry and have been
found to have a wide range of biological activities, including antitumor, antiinflammatory, and antimicrobial properties.52 PhI derivatives are also used to interact
with liver receptors that are involved in the regulation of cholesterol, lipid and glucose
metabolism.53 In industry, PhI is used in plastics, plasticizers, and is also used in the
synthesis of peptides and as a masked source for amines.54
Phthalimide, C6H4(CO)2NH, or isoindole-1,3-dione (IUPAC) has a melting point of
237-238 °C.55 PhI is a solid white crystal and can be obtained by heating phthalic
anhydride with ammonia or another amine source, such as ammonium carbonate or
ammonium acetate.56 The vapor pressure of PhI at 90°C is ~0.01 Torr57, sufficient to
measure the rotational transitions using pulsed-beam Fourier transform (PBFT)
microwave spectroscopy. The crystal structure of PhI was initially determined by Matzat
using data collected from the mineral kladnoite58 and the IR spectrum was measured by
Binev et al.59 In order to gain further insight into the molecular structure, Glidewell et al.
performed an X-ray crystallography analysis on PhI that was crystallized with pyridine.60
However, due to the packing effects and distortions within crystal structures of
molecules, it is important to measure the pure rotational spectrum of PhI in an attempt
obtain accurate gas phase structure.
89
5.2.2 MICROWAVE MEASUREMENTS
The phthalimide sample was purchased from Sigma Aldrich (99%) and was used
without further purification. A pulsed-beam Fourier transform microwave spectrometer,
described previously, was used to make microwave measurements in the 4.8–9.5 GHz
range for the parent isotopologue and these transitions are shown in Table 5.2.1.
Table 5.2.1 Measured rotational transitions of the parent isotopologue shown in MHZ.
J′ Ka’ Kc’ F’
3 1 3 4
3 1 3 2
3 1 3 3
3 1 3 3
3 0 3 2
3 0 3 4
3 0 3 2
3 0 3 3
3 0 3 3
4 2 3 4
4 2 3 5
4 2 3 3
3 2 2 2
3 2 2 4
3 2 2 3
3 2 2 3
3 2 2 2
3 1 2 2
3 1 2 4
3 1 2 3
4 1 4 5
4 1 4 3
4 1 4 4
3 2 1 2
3 2 1 4
3 2 1 3
4 0 4 5
4 0 4 3
4 0 4 4
2 2 0 1
2 2 0 3
J″ Ka” Kc” F”
2 1 2 3
2 1 2 1
2 1 2 2
2 1 2 3
2 0 2 2
2 0 2 3
2 0 2 1
2 0 2 2
2 0 2 3
4 0 4 4
4 0 4 5
4 0 4 3
2 2 1 1
2 2 1 3
2 2 1 3
2 2 1 2
2 2 1 2
2 1 1 1
2 1 1 3
2 1 1 2
3 1 3 4
3 1 3 2
3 1 3 3
2 2 0 1
2 2 0 3
2 2 0 2
3 0 3 4
3 0 3 2
3 0 3 3
1 0 1 1
1 0 1 2
90
obs
o-c
4885.647
4885.773
4885.932
4887.012
5057.851
5059.259
5059.336
5059.637
5060.568
5076.449
5077.656
5077.972
5730.793
5731.123
5731.123
5731.703
5731.703
6285.845
6286.060
6286.374
6368.981
6369.065
6369.185
6402.812
6403.096
6403.328
6437.139
6437.206
6437.383
7194.918
7194.940
-0.001
0.002
-0.004
-0.002
-0.004
-0.002
0.008
0.010
-0.005
-0.003
-0.005
0.000
-0.006
0.000
0.000
-0.002
-0.002
-0.002
0.000
0.002
-0.005
0.002
0.003
-0.000
0.005
-0.002
-0.004
0.003
-0.002
0.001
0.005
4
4
4
4
4
5
5
5
5
5
5
4
4
4
4
5
5
5
6
6
6
6
6
6
2
2
2
2
2
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
1
0
0
0
3
3
3
3
3
5
5
5
5
5
5
3
3
3
3
4
4
4
6
6
6
6
6
6
3
3
5
4
4
6
4
5
6
4
5
3
3
5
4
4
6
5
7
5
6
7
5
6
3
3
3
3
3
4
4
4
4
4
4
3
3
3
3
4
4
4
5
5
5
5
5
5
2
2
2
2
2
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
1
0
0
0
2
2
2
2
2
4
4
4
4
4
4
2
2
2
2
3
3
3
5
5
5
5
5
5
2
3
4
3
4
5
3
4
5
3
4
2
4
4
3
3
5
4
6
4
5
6
4
5
7468.723
7468.723
7468.799
7469.146
7469.146
7813.517
7813.568
7813.672
7834.351
7834.396
7834.499
7993.887
7993.953
7993.988
7994.350
9088.837
9088.871
9089.131
9242.336
9242.377
9242.445
9247.940
9247.975
9248.051
0.008
0.008
-0.005
-0.003
-0.003
-0.002
-0.005
0.009
0.000
-0.005
-0.010
0.005
0.003
-0.005
-0.004
0.009
0.007
-0.000
-0.000
-0.001
-0.000
0.003
-0.003
0.002
Ne was used as the carrier gas and the backing pressure was set to ~ 1 atm.
Prior to the pulsed injection of the gaseous sample, the pressure inside the microwave
cavity was maintained at 10−6 to 10−7 Torr and the pulsed valve was heated to ~125 –
130 °C in order to obtain sufficient vapor pressure of the sample to obtain a parent test
signal in one pulsed-beam cycle. The unique 13C isotopologues of PhI were measured
in the same way as the parent in the 4.8 – 6.5 GHz range. The labeling scheme used to
describe the isotopic substitutions is shown in Figure 5.2.1 and the measured rotational
transitions of all the 13C isotopologues are shown in Table 5.2.2.
91
Figure 5.2.1 Best fit structure showing fit bond lengths (top, in Å) and angles (bottom,
in °). Also shown are the a and b principle axes within the molecule.
Table 5.2.2 Measured rotational transitions of each unique 13C isotopologue shown in
MHz.
Rotational Transitions
J′ Ka’ Kc’ F’
J″ Ka” Kc” F”
3 1 3 4
2 1 2 3
3 1 3 2
2 1 2 1
3 1 3 3
2 1 2 2
3 0 3 4
2 0 2 3
3 0 3 2
2 0 2 1
3 0 3 3
2 0 2 2
4 1 4 5
3 1 3 4
4 1 4 3
3 1 3 2
4 1 4 4
3 1 3 3
4 0 4 5
3 0 3 4
4 0 4 3
3 0 3 2
4 0 4 4
3 0 3 3
13
obs
4882.766
4882.887
4883.056
5055.325
5055.406
5055.692
6364.763
6364.848
6364.964
6432.188
6432.255
6432.426
C 1&2
13
 o-c
obs
0.001
0.000
-0.004
-0.002
0.005
0.001
-0.002
0.002
-0.003
-0.004
0.003
0.003
4859.367
4859.490
4859.655
5030.741
5030.821
5031.106
6334.076
6334.165
6334.282
6400.922
6400.988
6401.160
92
C 3&6
13
 o-c
obs
0.001
0.003
-0.005
-0.004
0.003
0.001
-0.006
0.005
0.002
-0.001
0.003
-0.002
4831.116
4831.235
4831.403
5011.206
5011.273
5011.570
6302.040
6302.129
6302.241
6375.781
6375.841
6376.023
C 4&5
13
 o-c
obs
0.001
-0.002
-0.001
0.000
-0.000
0.001
-0.005
0.007
-0.000
-0.000
0.000
-0.002
4867.167
4867.290
4867.456
5039.398
5039.472
5039.767
6344.535
6344.619
6344.740
6411.909
6411.965
6412.155
C 7&8
 o-c
0.001
0.000
-0.004
-0.001
0.004
-0.001
-0.003
0.003
0.003
0.000
-0.005
0.003
5.2.3 CALCULATIONS
Ab initio and DFT calculations were performed using the Gaussian 09 suite on
the high performance computing system at the University of Arizona to obtain an
optimized gas phase equilibrium structure which was used to predict the rotational
transitions of PhI. Calculations were performed using MP2 and B3LYP methods with 6311++G** and aug-cc-pVQZ basis sets respectively for each method. The calculated
rotational and quadrupole coupling constants of each calculation were used in Pickett’s
SPCAT program to predict the rotational transitions of the parent isotopologue.
In order to predict the rotational constants of all the unique 13C isotopologues,
first the ratios between the experimentally determined parent rotational constants and
the MP2/6-311++G** calculated rotational constants were determined. After changing
the mass of the 13C atom within the molecular structure and recalculating the rotational
constants of the new structure, these rotational constants of the isotopologue were
multiplied by the previously determined experimental/calculated ratio to obtain corrected
rotational constants of the 13C isotopologues, which were within <1% of the final
experimentally fit values. These corrected rotational constants and the quadrupole
coupling constants of the parent were used in the SPCAT program to predict the 13C
isotopologue rotational transitions.
5.2.4 ROTATIONAL CONSTANTS
The rotational constants for the parent and all unique 13C isotopologues were
determined using Pickett’s SPFIT program and these results are shown in Table 5.2.3.
While fitting the measured rotational transitions of the unique 13C isotopologues, the
centrifugal distortion constants (DJ and DJK) were held fixed to what was obtained from
93
the fit for the parent. The rotational constants obtained from the best fit gas phase
structure are shown with the experimentally fit rotational constants of all the
isotopologues and the measured – calculated differences (M – C) of these values in
Table 5.2.4. The calculated rotational constants of the best fit structure and its
isotopologues had a standard deviation of 0.14 MHz. THE B3LYP/aug-cc-pVQZ
calculated rotational constants were also much closer to the experimentally determined
values compared to the MP2/6-311++G** values, which can also be seen in Table
5.2.3.
94
Table 5.2.3 Fit rotational, centrifugal distortion and quadrupole coupling constants of the parent and unique 13C
isotopologues, as well as the MP2/6-311++G** calculated values for the parent.
Parent
A/MHz
1745.66545(95)
B/MHz
1199.33090(54)
C/MHZ
711.08644(29)
DJ/kHz
0.0120(65)
DJK/kHz
-0.050(81)
1.5χaa/MHz
2.719(10)
0.25(χbb- χcc)/MHz 1.2363(37)
N
55
σ/kHz
4
MP2/6311++G**
1731.668
1194.126
706.758
B3LYP/aug-ccpVQZ
1753.935
1202.057
713.239
2.9207
1.2916
2.9480
1.2745
13
C(1&2)
1742.7830(93)
1199.2423(53)
710.5795(10)
0.0120*
-0.050*
2.875(67)
1.222(12)
12
3
* Centrifugal distortion constants were held fixed to the parent during fits of 13C isotopologues
95
13
C(3&6)
1733.751(10)
1193.7412(60)
707.1382(11)
0.0120*
-0.050*
2.856(76)
1.222(13)
12
3
13
C(4&5)
1742.8865(81)
1180.4406(45)
703.94653(92)
0.0120*
-0.050*
2.785(59)
1.231(10)
12
3
13
C(7&8)
1737.6542(82)
1195.2699(47)
708.32901(94)
0.0120*
-0.050*
2.790(60)
1.248(10)
12
3
Table 5.2.4 Measured rotational constants compared to the rotational constants
calculated of the best fit structure, also showing the difference (M – C).
ISOTOPOLOGUE
Parent
A
B
C
13
C1&2
A
B
C
13
C3&6
A
B
C
13
C4&5
A
B
C
13
C7&8
A
B
C
MEASURED
1745.6654
1199.3309
711.0864
1742.7830
1199.2423
710.5795
1733.7512
1193.7412
707.1382
1742.8865
1180.4406
703.9465
1737.6542
1195.2699
708.3290
CALCULATED
1745.6989
1199.4121
710.9451
1742.8085
1199.2756
710.4174
1733.7742
1193.7870
706.9902
1742.9089
1180.4885
703.7989
1737.6740
1195.3256
708.1781
(M – C)
-0.0334
-0.0812
0.1413
-0.0255
-0.0333
0.1621
-0.0230
-0.0458
0.1480
-0.0224
-0.0479
0.1476
-0.0198
-0.0557
0.1509
5.2.5 MOLECULAR STRUCTURE
To obtain a best fit gas phase structure of the PhI molecule, which is a
vibrationally averaged structure consisting of equilibrium and ground state bond lengths
and angles, a nonlinear least squares fit was performed using the measured rotational
constants from each of the isotopologues. In the least squares fit, there were a total of 8
varied parameters in 2D Cartesian space. From the B3LYP/aug-cc-pVQZ calculation,
the structure of PhI was planar with C2v symmetry and to reduce the number of
parameters in the fit from 3D to 2D Cartesian space, the PhI molecule was restricted to
only be in the a-b plane. The inertial defect calculated from the experimental rotational
constants of the parent isotopologue was  = -0.175 amu Å2, confirming that the
structure of PhI is indeed planar with the calculated value close to zero. The negative
96
nonzero value indicates there are some slight out of plane vibration modes within PhI.
During the structure fit, all C – H and C = O bonds were fixed to the Gaussian calculated
equilibrium values and atoms H13 and N16 were held fixed to their calculated
equilibrium a-b coordinates fixing the N – H bond to its equilibrium value. Due to the C2v
symmetry in the molecule, each corresponding atom on opposite sides of the symmetry
axis (a-axis) were varied by the same variable a and b parameters, with the exception of
the parameter in the b-direction being varied by exactly opposite. With these constraints
and variable parameters set, the structure fit produced a best fit structure with a
standard deviation of only 0.14 MHz. A Kraitchman analysis was performed for all the
13
C isotopologues using the Kiesel KRA program. The best fit structure coordinates of
the parent are compared to the 13C coordinates determined by the Kraitchman analysis
in Table 5.2.5. The agreement between the Kraitchman coordinates and best fit
structure coordinates is very good, with the exception of the a-coordinate of C1 which is
different by ~0.04 Å and this difference can be accounted for the atom being closer to
the center of mass in the molecule, making the Kraitchman coordinates less reliable.
Table 5.2.5 Principle a and b coordinates of the best fit structure compared to the
coordinates of the unique 13C substituted atoms determined from a Kraitchman analysis.
Atom
C1
C2
C3
C4
C5
C6
C7
C8
H9
a
-0.218960
-0.219010
-1.400780
-2.598847
-2.598787
-1.400659
1.196171
1.196067
-1.389308
b
0.694229
-0.694261
-1.424120
-0.699165
0.699354
1.424193
1.164577
-1.164748
-2.510437
97
Krait-|a|
0.17(8)
Krait-|b|
0.69(31)
1.40(33)
2.60(94)
1.42(34)
0.70(25)
1.19(505)
1.16(493)
H10
H11
H12
H13
O14
O15
N16
-3.546617
-3.546506
-1.389086
2.978304
1.623990
1.624171
1.966051
-1.230599
1.230883
2.510510
-0.000169
-2.299981
2.299778
0.000168
The structural parameters obtained from the structure fit are shown in Tables
5.2.6 (bond lengths) and 5.2.7 (angles) compared to the B3LYP/aug-cc-pVQZ
calculated values, and these bond lengths and angles correspond to what is shown in
Figure 5.2.1. Because of the C2v symmetry of PhI, only the bond lengths and angles for
one side of the symmetry axis are shown, since the corresponding bond lengths and
angles for the opposite side of the a-axis are equal. The fit bond lengths and angles
compared to the B3LYP calculation are very close, only differing by ~0.005 Å for the
bond lengths and are exactly equal for all angles, with the exception of <(C1-C2-C3)
which increased by 1° from the calculation. Even though the determined gas phase
structure is vibrationally averaged between the equilibrium and ground state structures,
the differences are small and so the fit structure is an excellent representation of
phthalimide.
98
Table 5.2.6 Microwave fit values for bond lengths (in angstroms) compared to
B3LYP/aug-cc-pVQZ calculated values.
Interatomic Distance
r(C1-C2)
r(C1-C6)
r(C1-C7)
r(C7-N16)
r(C5-C6)
r(C4-C5)
Microwave Fit
Value (Å)
1.388
1.389
1.491
1.396
1.400
1.399
Calculated
Value (Å)
1.392
1.381
1.493
1.398
1.395
1.394
Table 5.2.7 Microwave fit values for angles (in degrees) compared to B3LYP/aug-ccpVQZ calculated values.
Angle
<(C1-C2-C3)
<(C1-C2-C8)
<(C3-C2-C8)
<(N16-C8-C2)
<(N16-C8-O14)
<(C2-C8-O14)
<(C7-N16-C8)
<(H13-N16-C8)
<(C2-C3-C4)
<(C2-C3-H9)
<(H9-C3-C4)
<(C5-C4-C3)
<(C5-C4-H10)
<(H10-C4-C3)
Microwave Fit Value
122
108
130
105
126
129
113
123
117
121
122
121
119
120
Calculated
121
108
130
105
126
129
113
123
117
121
122
121
119
120
5.2.6 DISCUSSION
The rotational spectrum of PhI was measured in the 4.8 to 9.5 GHz range using
pulsed-beam Fourier transform microwave spectroscopy. The rotational transitions
measured for the parent and all unique 13C isotopologues are given in Tables 5.2.1 and
5.2.2. Using the rotational constants determined from each of the measured
99
isotopologues, a vibrationally averaged ground state gas phase structure was
determined and is shown in Figure 5.2.1. Tables 5.2.5 – 5.2.7 show the best fit a-b
principle axes coordinates, the interatomic distances, and angles respectively. The best
fit structure obtained of PhI is in very good agreement with the crystal structure data
obtained previously, with the bond lengths only deviating by ~0.01 Å and angles varying
by ~0.1°. Obtaining a more complete gas phase structure will require the measurement
of deuterium substituted isotopologues.
100
5.3 4a,8a-AZABORANAPHTHALENE
5.3.1 INTRODUCTION
Interest has been growing in the amine-borane functional groups because of the
potential of this group to act as a hydrogen storage material.61,62 This group stems from
the ammonia borane molecule which is an air-stable solid with 19.6% (by weight) of
hydrogen. This groups ability to thermally63 and catalytically64 desorb H2 has been
significantly studied. The addition of carbon atoms to the amine-borane groups (CBN
materials) are currently being studied and have been shown to possess improved
thermal stability65 leading to improved efficiency66 as well as room temperature liquidphase behavior67 and facile regeneration.68 Aromatic hydrocarbons are of interest
because of the well-defined π-conjugation which can be utilized in areas such as
organic semiconductors69 and sensors.70 The insertion of the B-N group into aromatic
hydrocarbons is gaining interest because it provides different electronic properties.71,72
These molecules can be used for a number of different cross-coupling reactions and
also act as fluorophores with a distinct response to certain ions, enabling them to act as
chemosensors.73
Gas phase microwave spectroscopy provides an accurate method to determine
molecular structures. It also allows for identification of compounds and additional
understanding of the electronic charge distribution in molecules from the analysis of the
hyperfine structure, resulting in the nuclei’s electric quadrupole coupling strengths. BNcyclohexane is a cyclic CBN material with one BN substitution within the cyclohexane
ring.74 Recently, an attempt to determine the structural information of BN-cyclohexane
was carried out by microwave spectroscopy. Under the experimental conditions (heating
101
of sample and pulsed-valve in a Ne gas stream prior to a supersonic expansion of the
gaseous sample into a vacuum cavity) there was a loss of H2 and BN-cyclohexene was
produced and the spectra observed.75 Substituting the BN group into the quintessential
molecule benzene yields 1,2-dihydro-azaborine which has also been studied by gas
phase microwave spectroscopy.76 Structural studies regarding B-N bond distances of
substituted 1,2-azaborine derivatives using X-ray diffraction have shown that these
azaborine compounds have delocalized electronic structures consistent with aromatic
character.77 The experimental determination of nuclear quadrupole coupling strengths
allows for the determination of the valence p-orbital electron occupations on the B and
N nuclei using an extended Townes – Daily model.78,79 This results from this model
provides information about the aromatic character of these molecules by comparing the
determined electron occupations with the calculated natural bond orbital (NBO)
occupations for boron and nitrogen. Other molecules studied by microwave
spectroscopy containing the B-N substitution are N-Et-1,2-azaborine,80 aziridineborane,81 H3N-BF3,82,83 ammonia-borane,84 aminoborane,85,86 aminodifluoroborane,87
diaminoborane,88 and a van der Waals complex with HCN-BF3.89 The present work
extends the BN-substituted molecules studied to include yet another quintessential BN
substituted molecule, BN-naphthalene (4a,8a-azaboranaphthalene). A disordered X-ray
crystal structure was determined previously so the accuracy of the current structure is
limited.90 It would be important to determine accurate structural parameters and
characterize the aromatic character of BN-naphthalene using gas phase microwave
spectroscopy.
102
5.3.2 CALCULATIONS
A DFT computation was performed for BN-naphthalene to obtain an optimized
equilibrium structure using a B3LYP method with an aug-cc-pVTZ basis. This
computation was performed using the Gaussian 09 suite at the University of Arizona.
The calculated dipole moment was 1.6 D oriented along the b-axis. The calculated
rotational constants of the optimized equilibrium structure were used in Pickett’s SPCAT
program to obtain the predicted frequencies of the b-type transitions expected to be
observed due to the large b-dipole moment component. Once the rotational constants
were determined for the most abundant 11B14N isotopologue, a set of scale factors were
determined from the ratio of the experimentally determined rotational constants with the
optimized, calculated values. To predict the 11B13C isotopologue rotational constants,
first the moments of inertia were recalculated for the isotopologue after changing one of
the masses of 12C to that of 13C using Kisiel’s PMIFST program. These rotational
constants were multiplied by the set of scale factors determined from the 11B14N
isotopologue to obtain the predicted set of 11B13C isotopologue rotational constants.
These predicted rotational constants were within 1% of the final experimentally
determined values after the assignments of the rotational energy levels to the transitions
measured.
103
Figure 5.3.1 Electron density mapped with the electrostatic potential (Iso Val = 0.0004)
of A) naphthalene and B) BN-naphthalene from the total SCF density using B3LYP/augcc-pVTZ. Red is the most electron rich and blue is electron deficient.
Qualitative results regarding the electronic charge distribution of BN-naphthalene
were obtained by using the optimized B3LYP/aug-cc-pVTZ structure to calculate the
isosurface of total electron density (Iso Val = 0.0004) mapped with the electrostatic
potential onto the molecule using B3LYP/aug-cc-pVTZ on the Gaussian 09 suite. To
directly compare with its hydrocarbon analog, a similar calculation was carried out for
naphthalene. The electrostatic potentials mapped with electron density for naphthalene
and BN-naphthalene are shown in Figure 5.3.1A and 5.3.1B respectively. The color
scheme is such that the red indicates the most negative (or electron rich) and blue
represents the most positive (electron deficient) regions within the molecule. Boron’s
valence typically has three electrons which are capable of making three sigma bonds
using the three valence sp2 hybridized orbitals, leaving the p-orbital unoccupied.
Nitrogen’s valence has five electrons, making three sigma bonds with its sp2 hybridized
orbitals and a lone pair in the p-orbital. Since the electric field gradients in molecules
104
mostly depend on the p-electron density, useful information about the aromatic
character of BN-naphthalene is determined from the calculations and directly from the
experimentally determined quadrupole coupling strengths of 14N and 11B using the
extended Townes-Dailey analysis (more in section 5.3.4).
5.3.3 MICROWAVE MEASUREMENTS
The BN-naphthalene sample was synthesized at the University of Michigan using
the experimental details published by the Ashe lab.91 Microwave measurements on the
synthesized sample of BN-naphthalene were made in the 2-10.4 GHz range using a
Flygare-Balle type pulsed-beam Fourier transform microwave spectrometer that has
been described previously and also the large cavity Flygare-Balle type microwave
spectrometer capable of measuring transitions down to 1 MHz.92 Before the pulse of the
molecular sample, the pressure inside the vacuum cavities of the spectrometers were
maintained at 10-6 to 10-7 Torr. Ne was used as the carrier gas and before passing over
the molecular sample, the Ne was passed through an OMI-1 purifier tube that was
purchased from Sigma Aldrich. The backing pressure of the Ne was maintained at
about 1 atm.
Table 5.3.1 Measured rotational transitions of the 11B14N isotopologue. Values shown
in MHz.
11
J′ Ka’ Kc’ F1’ F’
1 1 0 3 2
1 1 0 1 1
1 1 0 1 1
1 1 0 3 2
J″ Ka” Kc” F1” F”
1 0 1 1 1
1 0 1 3 2
1 0 1 2 1
1 0 1 3 3
105
B14N
obs
o-c
2179.7240
2179.7813
2179.9329
2179.9571
-0.0060
0.0018
0.0030
-0.0024
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
3
3
3
3
3
3
5
5
5
3
3
6
6
2
2
2
2
2
2
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
0
0
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
3
3
3
3
3
3
3
1
1
4
4
0
0
0
0
0
0
0
2
3
3
2
2
3
2
2
4
1
4
2
2
3
3
3
1
3
3
2
3
3
2
2
3
3
3
4
5
4
2
3
4
6
6
2
4
5
8
1
4
1
1
4
1
4
3
4
4
3
1
4
3
2
4
2
3
3
3
4
2
2
2
3
4
3
3
3
2
3
4
2
2
5
4
4
2
2
4
7
5
2
4
4
9
2
4
1
1
3
1
4
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
0
0
0
0
0
2
2
2
2
2
2
5
5
5
3
3
6
6
2
2
2
2
2
2
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
0
0
0
0
0
2
2
2
2
2
2
4
4
4
2
2
5
5
1
1
1
1
1
1
1
1
3
2
3
3
3
2
1
3
1
1
1
4
4
2
2
2
4
2
3
3
2
2
2
2
2
2
3
4
3
1
3
4
7
7
2
4
5
8
2
3
1
3
3
1
4
2
4
3
2
2
4
3
1
4
1
2
2
4
5
3
1
3
3
3
2
3
2
3
2
3
3
1
4
3
3
1
2
4
8
6
3
3
4
9
1
3
2
2
3
1
3
106
2180.2341
2180.3198
2180.8807
2181.1696
2246.0699
2246.1470
2246.6648
2246.7358
2247.3151
2247.4661
2562.9129
2563.1467
2563.3627
2563.9003
2563.9272
2563.9517
2563.9928
2564.0394
2564.1451
2564.7382
2564.8827
3904.6352
3904.6973
3904.9352
3905.0188
3905.4868
4484.1528
4484.4399
4484.5142
4484.5903
4484.6792
4484.7446
5011.6021
5011.7275
5011.7778
5248.8096
5249.3145
5302.4146
5302.4692
5562.0176
5562.1392
5562.2998
5562.3691
5562.4224
5562.4722
5562.7515
0.0042
-0.0030
-0.0018
-0.0017
-0.0032
-0.0066
0.0018
-0.0098
-0.0041
0.0022
0.0016
0.0018
-0.0046
0.0000
0.0047
-0.0026
0.0004
0.0022
-0.0002
0.0036
-0.0048
0.0008
0.0078
-0.0005
0.0059
-0.0068
0.0077
-0.0025
-0.0083
0.0047
0.0038
-0.0005
-0.0026
-0.0038
0.0046
-0.0009
0.0027
-0.0023
-0.0028
-0.0065
0.0001
0.0046
0.0040
-0.0033
-0.0009
-0.0044
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
3
3
3
3
3
3
3
0
2
2
2
2
3
3
3
3
4
4
5
5
5
5
3
3
3
3
3
3
3
2
2
4
2
2
3
2
4
4
4
3
5
6
4
7
6
4
6
7
5
5
6
1
3
4
3
3
3
2
5
3
4
2
5
5
4
6
7
4
6
6
4
5
7
2
1
1
3
3
2
2
4
4
3
3
4
4
4
4
5
5
5
5
5
5
5
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
2
2
2
2
2
2
1
1
1
3
3
2
2
4
4
3
3
4
4
4
4
4
4
4
4
4
4
4
2
3
3
2
2
2
1
3
3
5
2
4
5
3
5
7
4
6
5
5
5
6
1
2
4
2
3
3
2
4
2
4
1
4
4
4
5
6
3
6
6
4
6
7
5563.0088
5629.4268
5629.6841
7076.6250
7076.8428
7201.3242
7201.3672
7800.8184
7800.9487
8675.9053
8676.3770
10128.1406
10128.2158
10128.6934
10128.7666
10397.6445
10397.6816
10397.8994
10397.9766
10398.0127
10398.0547
10398.0947
-0.0030
0.0047
0.0023
0.0006
0.0010
0.0023
-0.0037
0.0009
0.0058
-0.0028
0.0084
-0.0007
0.0030
0.0012
-0.0065
-0.0022
-0.0061
-0.0002
0.0064
-0.0002
-0.0078
0.0073
Table 5.3.2 Measured rotational transitions of the 10B14N isotopologue. Values shown
in MHz.
10
J′ Ka’ Kc’ F1’ F’
1 1 1 3 2
1 1 1 4 3
1 1 1 4 5
1 1 1 2 3
3 0 3 4 5
3 0 3 4 3
3 0 3 5 6
3 0 3 3 3
3 0 3 3 4
3 0 3 4 3
3 0 3 3 4
3 0 3 2 2
3 0 3 2 2
3 0 3 5 5
3 0 3 4 3
3 0 3 4 5
J″ Ka” Kc” F1” F”
0 0 0 3 3
0 0 0 3 2
0 0 0 3 4
0 0 0 3 2
2 1 2 5 5
2 1 2 2 2
2 1 2 5 5
2 1 2 1 2
2 1 2 5 5
2 1 2 2 2
2 1 2 2 3
2 1 2 1 1
2 1 2 1 2
2 1 2 5 6
2 1 2 3 3
2 1 2 3 4
107
B14N
obs
o-c
3917.3203
3917.4241
3917.7371
3918.1902
4476.5693
4476.7778
4476.6436
4476.6709
4476.7007
4476.7778
4476.8572
4476.8945
4476.9370
4476.9839
4477.0952
4477.1748
0.0078
-0.0007
0.0000
-0.0061
-0.0024
-0.0086
-0.0060
0.0005
0.0077
-0.0086
-0.0052
-0.0085
0.0053
0.0012
0.0027
-0.0064
3
3
3
3
3
2
2
2
2
2
2
4
4
4
4
4
4
4
4
3
3
3
4
4
4
4
4
4
4
5
5
5
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
3
3
3
3
3
2
2
2
2
2
2
4
4
4
4
4
4
4
4
3
3
3
4
4
4
4
4
4
4
5
5
5
2
2
2
6
5
4
4
3
4
3
4
2
6
5
4
6
2
4
2
5
2
6
5
3
4
3
6
5
7
5
7
4
3
1
2
7
6
3
5
2
3
3
4
1
5
5
5
6
1
4
1
5
1
6
4
2
3
2
5
5
6
6
8
5
2
2
2
2
2
1
1
1
1
1
1
3
3
3
3
3
3
3
3
2
2
2
3
3
3
3
3
3
3
4
4
4
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
2
2
2
1
1
1
1
1
1
3
3
3
3
3
3
3
3
2
2
2
3
3
3
3
3
3
3
4
4
4
1
2
2
5
4
2
4
2
4
4
3
0
3
6
3
6
1
3
2
5
1
5
2
1
4
2
5
4
6
6
6
4
2
1
1
6
5
2
4
2
3
3
4
1
4
6
4
7
1
4
1
6
0
5
3
2
4
3
5
4
5
7
7
5
4477.2212
4477.2598
4477.3032
4477.3418
4477.3799
5643.2259
5643.3608
5643.4510
5643.8789
5644.0732
5644.1519
6686.6099
6686.7041
6686.7754
6686.8633
6686.9263
6686.9819
6687.0615
6687.2593
7218.1172
7218.2871
7218.4150
8694.4141
8694.7432
8694.8789
8695.0029
8695.1221
8695.2275
8695.4561
8805.0645
8805.1650
8805.3037
-0.0042
-0.0063
-0.0042
-0.0044
-0.0066
-0.0052
0.0010
-0.0021
0.0049
-0.0012
-0.0085
0.0033
0.0049
0.0019
0.0021
-0.0025
-0.0040
-0.0017
0.0042
0.0032
0.0032
-0.0073
-0.0004
0.0038
0.0041
-0.0039
0.0000
-0.0028
-0.0089
0.0050
0.0075
0.0026
Sufficient vapor pressure was obtained of the BN-naphthalene sample at room
temperature and this provided a single shot signal of the 0 to 1 b-type rotational
transition of the 11B14N isotopologue; these isotopologue transitions are shown in Table
5.3.1. The transitions from the 10B14N isotopologue were also measured at room
temperature and these transitions are shown in Table 5.3.2. 13C11B transitions were
measured at room temperature and the 11B15N transitions were measured at
108
temperature of 35 °C; these transitions are shown in Tables 5.3.3 and 5.3.4
respectively. All transitions were measured under natural abundance concentrations of
each isotope and an example of transitions from the 10B14N, 11B13C4 or 13C12, and
11
B15N isotopologues are shown in Figure 5.3.2.
Figure 5.3.2 Example transitions showing the hyperfine splitting from the 10B14N
(stimulation at 5643.680 MHz, 129 pulsed beam cycles), 11B13C4 or 13C12 (stimulation
at 3887.160 MHz, 2436 pulsed beam cycles), and 11B15N (stimulation at 5619.530 MHz,
7803 pulsed beam cycles) isotopologues.
109
Table 5.3.3 Measured rotational transitions of the singly substituted 13C11B
isotopologues. Values shown in MHz.
Energy Level Assignments
J′ Ka’ Kc’ F1’
J″ Ka” Kc” F1”
F’
F”
1 1 1 3 3
0 0 0 2 3
1 1 1 2 3
0 0 0 2 2
1 1 1 2 2
0 0 0 2 3
1 1 1 1 2
0 0 0 2 3
1 1 1 2 2
0 0 0 2 1
1 1 1 3 4
0 0 0 2 3
1 1 1 1 1
0 0 0 2 1
2 1 2 1 1
1 0 1 1 1
2 1 2 2 1
1 0 1 2 1
2 1 2 3 3
1 0 1 2 3
2 1 2 2 1
1 0 1 3 2
2 1 2 2 3
1 0 1 3 4
2 1 2 2 2
1 0 1 2 1
2 1 2 2 3
1 0 1 3 2
2 1 2 1 2
1 0 1 1 1
2 1 2 4 5
1 0 1 3 4
2 1 2 4 4
1 0 1 3 4
2 1 2 3 2
1 0 1 2 2
3 1 3 3 4
2 0 2 3 3
3 1 3 4 3
2 0 2 2 2
3 1 3 3 3
2 0 2 1 2
3 1 3 3 3
2 0 2 3 3
3 1 3 2 2
2 0 2 4 3
3 1 3 3 3
2 0 2 3 2
3 1 3 3 3
2 0 2 3 4
3 1 3 5 4
2 0 2 3 3
3 1 3 5 4
2 0 2 4 5
3 1 3 2 2
2 0 2 1 2
3 1 3 2 3
2 0 2 4 4
3 1 3 3 2
2 0 2 3 3
3 1 3 3 4
2 0 2 3 4
3 1 3 2 3
2 0 2 4 3
4 1 4 3 3
3 0 3 2 2
4 1 4 4 3
3 0 3 2 2
4 1 4 4 5
3 0 3 4 5
4 1 4 6 5
3 0 3 4 4
4 1 4 6 5
3 0 3 3 4
4 1 4 3 4
3 0 3 3 3
4 1 4 6 5
3 0 3 4 5
11
B13C1&13
obs
11
o-c
obs
o-c
11
B13C3&9
obs
o-c
3860.496
-0.000
11
B13C4&12
obs
o-c
3885.691 -0.003
3885.994 -0.001
3886.059
0.004
3866.099 -0.000
3887.025 0.006
3887.091 -0.006
5581.264
5581.341
0.001
0.001
5591.966 -0.007
5592.029 -0.002
5592.112 -0.009
5592.212 -0.018
5592.240 0.003
5592.273 -0.006
5592.323 0.004
7147.654
7147.700
5573.487
0.003
5573.567 0.001
5573.734 -0.009
5581.576 0.004
7143.693 -0.005
5592.395 -0.018
7143.865 -0.007
7144.029 0.003
7144.100 -0.002
7147.979 -0.003
0.005
0.005
7134.095
-0.001
7148.014 0.004
7148.221 -0.002
7148.648 0.000
7148.691 -0.009
7133.712 -0.006
7133.783 0.008
7133.929 0.005
7134.008 0.003
7148.987 -0.003
8606.540
8607.016 -0.005
8608.798 -0.003
8598.618
8608.899 -0.007
8610.130
8610.332
8609.342 -0.005
110
B13C2&8
0.000
0.005
0.003
0.000
Table 5.3.4 Measured rotational transitions of the 11B15N isotopologue. Values shown
are in MHz.
J′ Ka’ Kc’ F’
1 1 1 3
2 1 2 4
3 1 3 2
4 1 4 3
4 1 4 3
5 1 5 4
J″ Ka” Kc” F”
0 0 0 2
1 0 1 3
2 0 2 1
3 0 3 2
3 0 3 3
4 0 4 4
obs
o-c
3896.0701
5619.2651
7189.5835
8663.3870
8664.1787
10115.7393
0.0000
-0.0002
0.0003
0.0025
-0.0027
0.0000
5.3.4 ROTATIONAL AND QUADRUPOLE COUPLING CONSTANTS
The rotational constants, centrifugal distortion constants and quadrupole coupling
strengths were determined using Pickett’s SPFIT program. The results are listed in
Table 5.3.5. The assignments of the transitions with either 10B or 11B and 14N are
assigned using the quantum numbers |J Ka Kc F1 F>. These quantum numbers arise
from the angular momentum coupling scheme IB + J = F1 and F1 + IN = F. For 11B, I=3/2,
the Pickett notation rounds the spin up to 2 which gives the integer numbers for F1 and
F in Tables 5.3.1, 5.3.3 and 5.3.4. In the case of 15N, the N quadrupole moment
collapses and the quantum numbers used in the energy level assignments are |J Ka Kc
F> where the angular momentum coupling is J + IB = F. The inertial defect calculated
from the experimental rotational constants of the 11B14N isotopologue is ∆ = -0.159 amu
Å2 which is consistent with a planar structure. The small negative nonzero value of the
inertial defect indicates the presence of out of plane vibrational modes within the
molecule. Its magnitude is larger than what was obtained for 1,2-dihydro-1,2-azaborine
(∆ = 0.02 amu Å2), which may affect the aromatic character of BN-naphthalene when it
deviates from planarity.
111
Table 5.3.5 Experimentally determined rotational, quadrupole coupling and centrifugal distortion constants of all
measured isotopologues.
11
A/MHz
B/MHz
C/MHZ
B 1.5χaa/MHz
B 0.25(χbbχcc)/MHz
N 1.5χaa/MHz
N 0.25(χbbχcc)/MHz
DJ/kHz
N
σ/kHz
B14N
3042.71275(43)
1202.70657(35)
862.22013(35)
-3.9221(75)
-0.9069(24)
10
B14N
3054.3775(21)
1202.72868(79)
863.26917(36)
-3.809(21)
-1.0013(60)
2.5781(61)
-0.1185(17)
0.0565(96)
72
4
11
B13C1&13
3032.8954(44)
1186.525(12)
853.0973(17)
-3.9221*
-0.9069*
11
B13C2&8
3008.9390(65)
1198.597(16)
857.4037(23)
-3.9221*
-0.9069*
B13C3&9
3004.3924(83)
1197.557(22)
856.3471(30)
-3.9221*
-0.9069*
2.6324(99)
-0.0987(27)
2.5781*
-0.1185*
2.5781*
-0.1185*
0.0565*
48
5
0.0565*
16
5
0.0565*
10
4
* Quadrupole coupling and distortion constants were held fixed to the 11B14N isotopologue.
** Quadrupole coupling constants were held fixed to the B3LYP/aug-cc-pVTZ calculation for the 11B15N isotopologue
112
11
11
B13C4&12
3034.4177(80)
1185.175(23)
852.5212(31)
-3.9221*
-0.9069*
11
B15N
3034.4868(27)
1202.6225(95)
861.5671(11)
-3.8933**
-0.8129**
2.5781*
-0.1185*
2.5781*
-0.1185*
-
0.0565*
10
5
0.0565*
10
6
0.0565*
6
2
A B3LYP/aug-cc-pVTZ calculation was performed with BN-naphthalene to
determine the natural bond orbital electron occupancies of 14N and 11B. These orbital
electron populations are shown in Tables 5.3.6 and 5.3.7 for 14N and 11B respectively.
From the experimentally determined quadrupole coupling strengths of 14N and 11B, the
orbital occupations can be directly determined through the extended Townes-Dailey
analysis using sp2 hybridized orbitals around the nuclei. In order to perform the TownesDailey analysis in BN-naphthalene, it is necessary to know the atomic quadrupole
coupling constants for the 14N and 11B atoms due to one unpaired electron in the porbital. These values are listed in Gordy and Cook and are -11.2 MHz for 14N and -5.4
MHz for 11B. In order to calculate the orbital occupations, a value for the occupation of
the pc-orbital needs to be chosen (which is chemically reasonable and should not
exceed more than 2 for the p-orbital). From following the mathematics in the extended
analysis described in the literature, the occupations of either NB, number of electrons in
the valence of N in the N-B σ-bond (in the case of N), or NN, number of electrons in the
valence of B in the N-B σ-bond and the sum of the occupations of the adjacent C atoms
(NC+NC) next to either the N or B nucleus are calculated. The results from the TownesDailey analysis from 14N and 11B are shown with the NBO calculated results in Tables
5.3.6 and 5.3.7 respectively.
113
Table 5.3.6 Townes-Daily determined and NBO calculated (using B3LYP/aug-ccpVTZ) electron orbital occupancies for N using sp2 hybridized orbitals. The bolded
values are the best agreement between the NBO calculation and the Townes-Dailey
analysis.
Orbital
Occupations
N pc
NB (sp2)
NC+NC
(sp2+sp2)
Ntotal
Charge
Townes-Dailey
NBO
1.2
1.3
1.3
1.4
1.4
1.5
1.45
1.6
1.5
1.6
1.6
1.7
1.7
1.8
2.1
4.6
0.37
2.3
5.0
0.0
2.5
5.4
-0.43
2.6
5.6
-0.63
2.7
5.8
-0.83
2.9
6.2
-1.2
3.1
6.6
-1.6
1.4
1.5
2.5
5.4
-0.43
Table 5.3.7 Townes-Daily determined and NBO calculated (using B3LYP/aug-ccpVTZ) electron orbital occupancies for B using sp2 hybridized orbitals. The bolded
values are the best agreement between the NBO calculation and the Townes-Dailey
analysis.
Orbital
Occupations
N pc
NN (sp2)
NC+NC
(sp2+sp2)
Ntotal
Charge
Townes-Dailey
NBO
0.00
0.32
0.10
0.42
0.20
0.52
0.30
0.62
0.40
0.72
0.50
0.82
0.60
0.92
1.4
1.7
1.3
1.6
2.1
0.87
1.8
2.5
0.47
2.0
2.9
0.10
2.2
3.3
-0.33
2.4
3.7
-0.73
2.6
4.1
-1.1
0.23
0.46
1.4
2.1
0.89
5.3.5 GAS PHASE STRUCTURE
Gas phase structural parameters were obtained for BN-naphthalene using a
nonlinear least squares fitting program with the rotational constants determined from the
seven unique isotopologues measured. This structure fitting program varies the
Cartesian coordinates of the atoms within the molecule and a “best fit” structure is
114
obtained. The best fit structure is determined when the structure fit yields calculated
rotational constants closest to the experimentally fit values. From the B3LYP/aug-ccpVTZ calculation of BN-naphthalene, the structure was predicted to be planar with C2v
symmetry. The calculated inertial defect from the experimentally determined rotational
constants is ∆ = -0.159 amu Å2 confirming that the structure is indeed planar with some
out of plane vibrational motion.
In the structure fit, there were a total of 10 variable parameters representing
small changes in select atomic Cartesian coordinates in the a-b plane. The best fit
structure was fixed to be planar by setting all c-coordinates equal to zero due to the
experimental value of the inertial defect. It was assumed that the symmetry of BNnaphthalene molecule is maintained and so the varied coordinates in the fit were
equivalent for corresponding atoms across the symmetry axis (B-N bond), with the
exception of the varied parameters in the a-direction which were opposite sign for each
corresponding C atom. The only fixed atom in the structure fit was N and the B atom
was varied by its own a and b variable parameters. The H atoms bonded to the C atoms
within the ring were varied by the same variable parameters as the C atom it was
bonded to, resulting in the C-H bond lengths to be fixed to optimized equilibrium values.
With these constraints and varied parameters set, the standard deviation of the
structure fit was 0.151 MHz. The best fit structure showing the bond lengths and angles
is shown in Figure 5.3.3.
115
Figure 5.3.3 Best fit structure showing bond lengths (Å) and angles (º). Only half of the
bond lengths and angles are shown in the cyclic ring structure due to the symmetry of
the molecule. All C-H bond lengths were held fixed to calculated equilibrium values and
so are not shown.
A Kraitchman analysis was also performed on all the isotopically substituted
atoms using the Kisiel KRA program. The atomic coordinates of the best fit structure
and of each isotopically substituted atom are shown in Table 5.3.8. The Kraitchman
determined coordinates agree very well with the coordinates obtained from the best fit
structure, with the exception of the a-coordinate of both the B and N atoms. These
atoms lie along the b-axis, thus making the Kraitchman calculated coordinates
unreliable. The differences between the experimentally determined rotational constants
are compared with the calculated best fit structure values from each isotopologue in the
116
in Table 5.3.9. A comparison of the B-N bond length in BN-naphthalene and other B-N
substituted molecules are shown in Table 5.3.10.
Table 5.3.8 Principle axes coordinates of the best fit structure being compared with
the Kraitchman determined coordinates for each of the isotopically substituted atoms.
Values shown are in Å.
Atom
C1
C2
C3
C4
C8
C9
C12
C13
H5
H6
H7
H10
H11
H14
H15
H16
B17
N18
a
-2.400
-1.203
-1.354
-2.499
1.203
1.354
2.499
2.400
1.122
-3.294
-1.122
-1.476
-3.492
1.476
3.492
3.294
0.000
0.000
b
-0.743
-1.373
1.466
0.689
-1.373
1.466
0.689
-0.743
-2.451
-1.349
-2.451
2.543
1.125
2.543
1.124
-1.350
0.796
-0.674
117
Krait-|a|
2.39654(71)
1.1933(14)
1.3762(13)
2.49610(75)
1.1933(14)
1.3762(13)
2.49610(75)
2.39654(71)
Krait-|b|
0.7431(20)
1.3723(11)
1.4642(10)
0.6835(22)
1.3723(11)
1.4642(10)
0.6835(22)
0.7431(20)
0.2790(54)
0.078*i(20)
0.7947(19)
0.6746(22)
Table 5.3.9 Comparison of rotational constants obtained from the best fit structure
compared with the experimentally determined values for each isotopologue and their
differences. The standard deviation of the structure fit was 0.151 MHz. Values shown
are in MHz.
ISOTOPOLOGUE
11 14
B N
A
B
C
10 14
B N
A
B
C
11 13
B C1
A
B
C
11 13
B C13
A
B
C
11 13
B C2
A
B
C
11 13
B C8
A
B
C
11 13
B C3
A
B
C
11 13
B C9
A
B
C
11 13
B C4
A
B
C
11 13
B C12
A
B
C
11 15
B N
A
B
C
MEASURED
3042.7128
1202.7066
862.2201
3054.3775
1202.7287
863.2692
3032.8954
1186.5250
853.0973
3032.8954
1186.5250
853.0973
3008.9390
1198.5970
857.4037
3008.9390
1198.5970
857.4037
3004.3924
1197.5570
856.3471
3004.3924
1197.5570
856.3471
3034.4177
1185.1750
852.5212
3034.4177
1185.1750
852.5212
3034.4868
1202.6225
861.5671
118
CALCULATED
3042.7609
1202.8299
862.0529
3054.4633
1202.8299
862.9896
3032.9559
1186.6062
852.9142
3032.9562
1186.6062
852.9142
3008.9715
1198.6875
857.2026
3008.9718
1198.6873
857.2026
3004.3468
1197.5846
856.2633
3004.3479
1197.5832
856.2627
3034.3442
1185.2602
852.3281
3034.3442
1185.2595
852.3277
3034.5579
1202.8299
861.3932
(M – C)
-0.0482
-0.1233
0.1672
-0.0858
-0.1012
0.2796
-0.0605
-0.0812
0.1831
-0.0608
-0.0812
0.1831
-0.0325
-0.0905
0.2011
-0.0328
-0.0903
0.2011
0.0456
-0.0276
0.0838
0.0445
-0.0262
0.0844
0.0735
-0.0852
0.1931
0.0735
-0.0845
0.1935
-0.0711
-0.2074
0.1739
5.3.6 DISCUSSION
The microwave spectra were measured for seven unique isotopologues of BNnaphthalene using pulsed beam Fourier transform microwave spectroscopy. From the
best fit structure, bond lengths and angles of the ring system were determined. Even
though the C-H bond lengths were held fixed to optimized equilibrium values, the
structure obtained is a reasonably accurate representation of the molecule in its ground
state. The B-N bond length determined from the structure fit was 1.470 Å. This bond
length agrees fairly well with the X-ray determined B-N length of 1.461 Å, only differing
by about 0.01 Å. Comparing the remaining bond lengths of the rings in the microwave
and X-ray structures, the C1-C2, C1-C4 and C3-C4 bond lengths also all agree fairly
well with the X-ray structure, again only deviating by about 0.01 Å. The C3-B17 bond in
the microwave structure has the largest deviation when compared with the X-ray
structure with a difference of 0.055 Å. The differences between these two structures
arise most likely due to the X-ray crystal structure being an averaged structure of the
disordered BN-naphthalene molecules within the crystal.
119
Table 5.3.10 A comparison of B-N bond distances of BN-naphthalene and other
previously studied molecules containing the B-N bond.
r(B-N) Interatomic Microwave Fit Value
Distances
(Å)
BN-naphthalenea
1.470
BN-cyclohexeneb
c
1,2-dihydro-azaborine
1.45
H3NBF3d
1.59
BH3NH3e
1.6576
H2NBH2f
1.391
HCN-BF3g
2.47
a
This work
b
Calculated
Value (Å)
1.475
1.40
1.437
-
Reference 75, calculated value obtained using B3LYP/aug-cc-pVTZ
c
Reference 76, calculated value obtained using MP2/6-311+G(d,p)
d
Reference 83
e
Reference 84
f
Reference 85
g
Reference 89
When comparing the B-N bond lengths of the different types of molecules with BN substitutions, listed in Table 5.3.10, the microwave structure bond length of BNnaphthalene agrees with the other B-N bond lengths where there is some π-donation
from the N p-orbital to the empty p-orbital on B. As a result there is some double bond
character between the B and N, which shortens the bond length. The boron nucleus has
an empty p orbital within the π-system that can accept electron density to maintain its
aromatic character within BN-naphthalene. As the donation of this lone pair on nitrogen
becomes less, the bond length increases which can be seen in the molecules H3NBF3,
BH3NH3, and a van der Waals complex HCN-BF3. Because the bond length determined
120
for BN-naphthalene (1.47 Å) is intermediate between H2NBH2 (1.391 Å, double bond)
and BH3NH3 (1.6576 Å, single bond), it can be concluded there is some aromatic bond
character between the B and N in BN-naphthalene. Another criteria for the aromatic
character in molecules, the planarity, can be directly determined from the analysis of the
microwave spectra by calculating the inertial defect using the experimental rotational
constants. BN-naphthalene has a larger magnitude inertial defect (∆ = -0.159 amu Å2)
when compared with 1,2-dihydro-1,2-azaborine (∆ = 0.02 amu Å2). This is likely due to
BN-naphthalene being a much more extended molecule, so the out of plane amplitudes
for the bending vibrations will be greater than for 1,2-azaborine. Regardless of the
larger magnitude inertial defect for BN-naphthalene, the value is still close enough to
zero indicating a fairly planar structure.
Since the bond length obtained from the best fit structure supports the
assumption that there is some π-character between B and N, natural bond orbital and
extended Townes-Dailey analyses were performed to determine the extent of πdonation from the N to the empty p-orbital on the B. The electron occupations
determined from the NBO analysis for N are 1.4 in the p-orbital, 1.5 in the sp2 hybridized
orbital making the σ-bond with B (NB) , and 2.5 for the sum of the electrons in the two
sp2 hybridized orbitals making the σ-bonds with the adjacent C atoms (NC+NC). With
these occupations the total valence around nitrogen was calculated to be 5.4 electrons
with a charge of -0.43. These NBO calculations agree very well with the Townes-Dailey
determined occupations when the occupation of the p-orbital on 14N was chosen to be
1.4 and this comparison is shown in Table 5.3.6. The orbital electron occupations of N
in BN-naphthalene is very similar to the occupations determined for 1,2-dihydro-1,2-
121
azaborine, which was shown to have similar properties when compared to other
aromatic N-containing molecules, such as pyrrole.93
The values of orbital occupations obtained by the NBO analysis of B are 0.23
electrons in the p-orbital, 0.46 electrons in the sp2 hybridized orbital making the σ-bond
with N (NN), and 1.4 electrons in the two sp2 hybridized orbitals making the σ-bonds with
the adjacent C atoms (NC+NC). With these occupations on B, the total valence was
calculated to be 2.1 electrons with a charge of +0.89. The agreement of the NBO
calculation with the extended Townes-Dailey analysis performed for 11B does not agree
as well as with 14N. It can be seen by the bolded values in Table 5.3.7 that the NBO
analysis agrees with occupations from the Townes-Dailey analysis when there are
between 0-0.2 electrons in the p-orbital. The sum of the NB and NN from the sigma bond
electron occupancies equal 2.02e- which is consistent with the bond population. Using
this as a constraint across the two analyses gives additional support to the designation
of 0.2 e- in the valence pc-orbital for boron. There may be some disagreement between
the NBO calculation and the extended Townes-Dailey analysis for 11B because of the
possibility of the B nucleus to also accept π-electron density from the adjacent carbon
atoms, which was not taken into account in the NBO calculation as this was calculated
for one resonance structure. It can be seen from the electrostatic potential map of BNnaphthalene in Figure 5.3.1B that there is a build-up of negative charge in the π-system
adjacent to the B nucleus. If the aromatic character in the molecule is maintained, then
there will also be donation of electrons into the empty p-orbital on B, which will change
the orbital electron occupancies and thus affect the analysis.
122
6. MICROWAVE SPECTRA OF DOUBLY HYDROGEN BONDED DIMERS
Hydrogen bonds are important interactions in biological and chemical processes.
The determination of gas phase molecular structures of heterodimers is crucial to
testing the predictive power available for these noncovalent interactions. For example,
the hydrogen bonding seen in DNA is important for the proper translation of the
information stored in DNA into functioning proteins. Furthermore, the secondary and
tertiary structures of proteins is largely dependent upon these hydrogen bonding
interactions. Studying these types of systems is important to obtain these benchmarks
so the theory can be improved upon and agree more accurately with experiment.
Hydrogen bonding is also observed in catalysis and many chemical reactions.
Understanding these interactions is critical so that synthetic chemists, for example, are
able to formulate and synthesize catalysts with increased enzymatic activity.
The proton tunneling dynamics between the two molecules in the dimer can be
studied using gas phase microwave spectroscopy. This proton tunneling phenomenon
can be observed in the microwave spectra in terms of splittings of transitions. These
splittings are similar to what is observed in the inversion of ammonia. Research
suggests that it is this proton tunneling motion in DNA base pairs that may give rise to
spontaneous point mutations, which may cause disease. Furthermore, microwave
spectroscopy is one of the best techniques to analyze this tunneling motion in
molecules due to the high resolution available. The importance of hydrogen bonding
interactions, accurate molecular structures and describing the dynamics in these
systems is of fundamental importance in all of chemistry and biochemistry and so
studying these small benchmarks is crucial to advance our understanding.
123
6.1 CYCLOPROPANECARBOXYLIC ACID – FORMIC ACID DIMER
6.1.1 INTRODUCTION
There has been recent interest growing in doubly and triply hydrogen bonded
complexes. These complexes are simple prototypes of doubly and triply hydrogen
bonded DNA base pairs, adenine – thymine and guanine – cytosine. The dynamics of
hydrogen bonding is also involved in the intricate formation of protein secondary
structures as well as in the most basic proton transfer within solutions. These hydrogen
bonded dimers are not static and some previously studied dimers have been shown to
exhibit proton tunneling dynamics, which may be associated with some types of genetic
mutations and disease.94,95 The dynamics of this proton tunneling process are best
observed and characterized through the analysis of the rotational spectrum measured
by microwave spectroscopy. Some of these previously studied hydrogen bonded dimers
by microwave spectroscopy include dimers formed between propiolic acid – formic
acid,96,97,98 acetic acid – formic acid,99 and the monoenolic tautomer of 1,2cyclohexanedione – formic acid (discussed in the next section).100 In the case of
propiolic acid – formic acid, proton tunneling was observed and details about the
dynamics were characterized. The tunneling may be due to the C2V(M) symmetry which
creates a symmetric double well potential energy surface allowing for the tunneling
motion to occur. Studying these carboxylic acid doubly hydrogen bonded dimers may
allow for more insight into this tunneling process and give better quantitative predictions
for the tunneling phenomena.
124
The simplest of these doubly hydrogen bonded systems is the formic acid
homodimer.101 The two equivalent forms of this dimer were found to interconvert
through a concerted tunneling motion of the two acidic protons. The potential energy
surface for this system has a classic double well potential, similar to that of ammonia
inversion and the systems of single proton tunneling as in malonaldehyde102,103,104,105
and tropolone.106,107 Microwave spectroscopy is the most suitable technique to study the
molecular structure and dynamics of many systems, but is restricted to molecules and
complexes with permanent electric dipoles, or in heterodimers of two carboxylic acids
as in the case of the dimer cyclopropanecarboxylic acid – formic acid (CPCA – FA)
discussed here.
6.1.2 MICROWAVE MEASUREMENTS
The rotational spectra was measured in the 4-11 GHz region for the doubly
hydrogen bonded dimer CPCA-FA. Microwave measurements were made using a
Flygare-Balle type pulsed-beam Fourier transform (PBFT) microwave spectrometer. The
CPCA (95 %) and FA (98 %) samples were purchased from Sigma Aldrich and the FAd1 (99.2% d) was purchased from CDN isotopes; each sample was used without further
purification. The samples were transferred to separate glass sample cells. The glass
sample cell containing the CPCA was connected directly to the pulsed-valve (General
Valve series 9) and was heated to ~70 °C. The cell containing the FA was placed in the
Ne gas line leading to the CPCA sample and the pulsed valve, seeding the FA vapor
into the carrier gas. This FA and Ne gas was pulsed into the cavity, picking up CPCA
vapor just before reaching the cavity. The FA sample (and also FA-d1) was first cooled
125
to about -8 °C before connecting to the gas line and the sample temperature was
maintained using a Peltier cooling device. The pressure inside the microwave cavity
was maintained at 10-6 to 10-7 Torr prior to the molecular beam pulse into the cavity.
The Ne carrier gas backing pressure was maintained at ~ 1 atm. The valve was set to
pulse at ~ 2 Hz. All measured transitions of the CPCA – FA dimer are given in Table
6.1.1 and examples of observed transitions from the 13C isotopologues are shown in
Figure 6.1.1. The labeling scheme used for the atoms in the dimer is shown in Figure
6.1.2.
Figure 6.1.1 Example transitions of the parent isotopologue (6965.580 MHz stimulation),
the 13C isotopologue at the C16 position (6876.240 MHz stimulation), and the 13C
isotopologue at the equivalent positions of C3 and C6 (6878.020 MHz stimulation) of the
404 – 505 transition (from left to right) taken at 300 pulsed-beam cycles for each
transition shown.
126
Table 6.1.1 Spectral assignment and frequencies for parent and 13C isotopologues of the cyclopropanecarboxylic acidformic acid dimer.
J'
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5
5
5
6
6
6
6
6
6
Ka' Kc' J'' Ka''
0
2
2
1
1
0
2
3
3
2
1
1
0
2
3
3
2
1
1
0
2
3
2
1
3
2
1
2
4
4
3
2
1
2
3
5
5
4
3
2
3
4
6
6
5
4
4
5
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5
5
0
2
2
1
1
0
2
3
3
2
1
1
0
2
3
3
2
1
1
0
2
3
2
1
Kc''
Parent
oc*
2
1
0
1
3
3
2
1
0
1
2
4
4
3
2
1
2
3
5
5
4
3
3
4
4191.421
4197.447
4203.475
4319.526
5429.595
5581.547
5595.418
5599.555
5599.648
5610.463
5757.559
6784.273
6965.732
6992.377
7000.724
7001.087
7022.376
7193.992
8137.229
8342.650
8388.072
8402.670
8440.285
8628.358
0
1
1
5
0
0
1
6
-5
0
3
-1
0
0
-1
-2
0
0
-3
-2
-5
2
0
-2
13
oo13
C(16)
c*
C(3&6) c*
a-type transitions
C(1)
oc*
13
oC(9) c*
D(17)
oc*
4261.910
5361.166
5509.598
2 4262.330
0 5362.955
1 5510.783
1 4291.032
-1 5394.770
2 5545.365
1 4316.691
1 5425.831
-1 5577.765
4
0
1
5305.745
5451.427
12
-1
5680.834
6698.874
6876.372
0 5681.396
-1 6701.116
0 6877.861
0 5719.599
0 6740.787
0 6920.702
-2 5753.775
0 6779.566
1 6960.994
0
0
0
6629.704
6804.090
3
-1
7098.244
-1 7098.947
-2 7146.600
1 7189.260
-3
7952.096
8150.128
-10
1
127
13
7
7
8
8
1
0
1
0
7
7
8
8
6
6
7
7
1
0
1
0
6
6
7
7
9488.217
2
9711.186
0
10837.018 3
11070.533 -1
9488.486
b-type transitions
1
6
2
1
1 0 0
0
4703.986
0
0
6 5 1
5
5569.666
0
1
2 1 0
1
6021.120
0
*observed-calculated frequencies in kHz
128
1
Rotational transitions from five 13C isotopologues of the CPCA – FA dimer were
measured under natural abundance which include the parent and four single 13C
substitutions at all unique carbon atom positions within the dimer. The 13C substitutions
at carbon atoms 3 and 6 were calculated to be equivalent, which would result in an
increased intensity in the observed transitions. These two positions are indeed
equivalent and a comparison of signal intensities of some isotopologue transitions are
shown in Figure 6.1.1.
Figure 6.1.2 Calculated structures of the low energy (top) and higher energy (bottom)
CPCA-FA conformers using B97D with aug-cc-pVTZ basis. Also shown superimposed
on the low energy conformer are the a and b principle axes and the visualization of the
parameter φ (phi) used in the structure fit.
129
There were 51 total rotational transitions measured for the lower energy
conformer shown in Figure 6.1.2 (top); 28 a-type transitions and 3 b-type transitions
were measured for the parent isotopologue and 7 a-type transitions were measured for
each of the four uniquely substituted 13C and deuterated isotopologues. The small
splittings observed in the transitions shown in Figure 6.1.1 were determined to be a
result of the Doppler Effect and not the proton tunneling motion. Rotational transitions
were searched for corresponding to the high energy conformer in Figure 6.1.2 (bottom),
however after significant scanning, transitions from this conformer not observed.
6.1.3 CALCULATIONS
Ab initio and DFT calculations to obtain an optimized equilibrium structure of the
low energy CPCA – FA conformer were performed using the Gaussian 09 suite using
B97D/aug-cc-pVTZ and MP2/aug-cc-pVTZ methods. The calculated a and b dipole
moments for this conformer shown in Figure 6.1.2 (top) were 1.4 and 0.2 D respectively
from the MP2 calculation. Due to the magnitudes of the dipole moment components, it
was expected that the a-type transitions would be the strongest. The calculated
rotational constants from the optimized equilibrium structure for this conformer were
used in the Pickett program, SPCAT, to calculate the a and b-type rotational transitions.
The values of the rotational constants from the optimized structure are shown in Table
6.1.2, along with the experimentally fit constants determined from the measured
transitions. A Kraitchman analysis using the Kisiel KRA program was performed on
each of the isotopically 13C and deuterium substituted atoms in the CPCA – FA dimer.
130
These Kraitchman coordinates are shown in Table 6.1.3, compared with the best fit gas
phase structure coordinates.
Table 6.1.2 Ab initio (MP2/aug-cc-pVTZ and B97D/aug-cc-pVTZ) spectroscopic
constants and dipole moments of the cyclopropanecarboxylic acid - formic acid dimer.
Type
A/MHz
B/MHz
C/MHz
µa(Debye)
µb(Debye)
µc(Debye)
B97D/aug-cc-pVTZ
4068.66
732.32
652.25
1.7
0.2
0.0
MP2/aug-cc-pVTZ
4038.00
747.56
663.19
1.4
0.2
0.0
Experiment
4045.42
740.58
658.57
Table 6.1.3 Structural coordinates of the CPCA – FA (low energy) dimer in Å from the
nonlinear least squares fit with a standard deviation of 1.13 MHz. Also shown are the
Kraitchman determined coordinates for each of the isotopically 13C substituted atoms.
Atom
C1
H2
C3
H4
H5
C6
H7
H8
C9
O10
O11
H12
H13
O14
O15
C16
H17
a
2.154
2.478
2.972
2.433
3.827
3.012
3.880
2.485
0.701
0.027
0.139
-4.022
-0.915
-2.840
-2.209
-3.022
-1.935
b
0.509
1.537
-0.587
-1.394
-0.215
-0.483
-0.083
-1.263
0.299
1.474
-0.767
0.506
1.258
-1.325
0.833
0.085
-1.645
c
Krait-|a|
0.021 2.1464(11)
0.053
0.745
2.9923(8)
1.218
1.289
-0.748
2.9923(8)
-1.251
-1.276
-0.002
0.661(5)
0.022
-0.037
0.006 4.1468(13)
0.005
-0.001
-0.001
0.001 3.08253(72)
0.012
131
Krait-|b|
0.5447(42)
Krait-|c|
0.03*i(8)
0.4674(53) 0.7440(34)
0.4674(53) 0.7440(34)
0.3354(97)
0.04(9)
0.476(12)
0.282(20)
0.190(12)
0.02(13)
A separate B97D/aug-cc-pVTZ calculation was performed to optimize the high
energy conformer’s geometry. Comparing two B97D calculations of each of the
conformers, the energy separation of the two was determined to be 219 cm-1, less than
what was calculated to be the energy separation of the CPCA monomers (~ 300 cm-1).
The energy separation between the two conformers of the CPCA monomer was small
enough so these transitions from this other conformer were observed previously. Based
on these calculations and previous results from the monomer, it was expected that the
high energy CPCA – FA conformer would be observed. However, after performing the
predictive calculations for rotational constants and transitions, no transitions were
observed after significant searching for these high energy conformer transitions.
6.1.4 ROTATIONAL CONSTANTS
The experimental rotational and centrifugal distortion constants for the parent low
energy conformer of the dimer, Figure 6.1.2 (top), were determined using the Pickett’s
program SPFIT and are given in Table 6.1.4. A similar analysis was carried out for all
remaining singly substituted 13C and deuterium substituted isotopologues. The
centrifugal distortion constants obtained from the parent were held fixed in the fits for
the 13C and D isotopologues. These results are also given in Table 6.1.4. The rotational
constants from the calculations and the experiment are compared in Table 6.1.2. The
MP2 calculation with the aug-cc-pVTZ basis yielded rotational constants within 1% of
the experimental results.
132
Table 6.1.4 Spectroscopic constants for the parent and 13C isotopologues of the CPCA
– FA dimer.
A/MHz
B/MHz
C/MHZ
∆J/kHz
∆JK/kHz
N
σ/kHz
13
13
13
13
Parent
C(16)
C(3&6)
C(1)
C(9)
4045.4193(16)
4044.16(21)
4021.03(25)
4035.98(22)
4041.76(37)
740.58380(14) 730.45455(16) 730.44765(18) 735.63679(17) 740.11049(30)
658.56760(23) 650.51344(17) 650.81382(20) 654.40357(19) 658.09839(33)
0.0499(16)
0.0499*
0.0499*
0.0499*
0.0499*
0.108(14)
0.108*
0.108*
0.108*
0.108*
31
7
7
7
7
2
1
1
1
2
D(17)
4035.84(66)
722.3152(32)
643.9651(12)
0.0499*
0.108*
7
6
* fixed at the values for the parent isotopologue
6.1.5 MOLECULAR STRUCTURE
A nonlinear least squares fit was performed to obtain a best fit gas phase
structure of the low energy conformer of the CPCA – FA dimer using the rotational
constants from the parent and each of the measured isotopologues. The input is the set
of Cartesian coordinates of the atoms within the structure of the dimer. These Cartesian
coordinates of the atoms are varied to produce a structure with rotational constants
closest to the experimental results, so the derived structure assumes a rigid rotor
approximation that is vibrationally averaged, due the C – H bond lengths being fixed to
optimized equilibrium values within the monomer structure. The standard deviation for
this structure fit on the CPCA – FA dimer was 1.13 MHz. In the fit, the coordinates of all
atoms for each monomer unit were held fixed to previously obtained structural values
for CPCA (discussed in chapter) and FA.108 There were only two variable parameters
used in the structure fit for this dimer, which represented the movement of the fixed
structure of the FA moiety in the a-b plane relative to the fixed center of mass of CPCA.
133
A third parameter, φ, is the angle of rotation in the a-b plane for the FA coordinates
using a standard rotation matrix. Figure 6.1.2 shows the relative motion the angle φ
invokes on the FA moiety. The angle φ was not a variable parameter in the fit, but
different trial values were tested. The structure with the smallest standard deviation (the
minimum in Figure 6.1.3) is reported and is referred to as the “best fit” structure. Figure
6.1.3 shows a plot of the fit standard deviation obtained with different test values of the
angle φ.
Figure 6.1.3 Plot showing the variation of the “best-fit” standard deviation for the
nonlinear least squares structure fit with the angle φ. The variation of the angle φ
represents the rotation of the FA moiety in the x-y Cartesian plane and changes the
relative lengths of the two hydrogen bonds.
The standard deviation of the structure fit significantly increases after a value
smaller than φ = -0.05 radians. At these small φ values, the FA moiety is rotated to an
unreasonable position relative to the CPCA molecule and clearly does not correspond
with experimental results as seen with the standard deviation. The deviation represents
134
the differences of the best fit structure’s rotational constants with the experimentally fit
values. The actual value of φ is less important compared with the differences in
hydrogen bond lengths which are directly correlated with φ. Comparing the optimized
equilibrium structure with the best fit structure obtained from the nonlinear least squares
fit, the hydrogen bond lengths and center of mass separation of each monomer are
listed in Table 6.1.5. The hydrogen bond lengths became very asymmetric in the best fit
structure and the center of mass separations of the monomers only increased by 0.02
Å.
Table 6.1.5 Interatomic distances obtained by fitting the experimental rotational
constants for six isotopologues in a nonlinear least squares fit. Hydrogen bond lengths
and COM separations are in Å.
Interatomic Distance Microwave Fit Value
r(H12-O14)
r(O11-H13)
COM Separation
1.36
2.25
4.11
Calculated
(MP2) Value
1.67
1.62
4.09
6.1.6 DISCUSSION
The pure rotational spectrum of the doubly hydrogen bonded dimer formed
between CPCA – FA has been measured using a PBFT microwave spectrometer and
all the measured rotational transitions were assigned to be associated with the low
energy conformer. Scans for the high energy conformer transitions for the dimer were
unsuccessful. The predicted energy difference between the two conformers was only
~200 cm-1, but may be larger as these high energy conformer transitions were not
observed. There may be steric interactions of the FA hydrogen bonding to CPCA which
135
may prevent the CPCA molecule in the high energy form to form the hydrogen bonded
dimer, even though this conformer of CPCA was observed with the monomer.
The Kraitchman calculated coordinates of the 13C atoms and the D atom are in
fair agreement with the best fit coordinates, with the exception of some coordinates
varying by ~0.1 Å and more for the D substituted atom. The errors in some of the
substituted coordinates are large, a result of the substituted atoms lying close to the
principle axes or center of mass within the dimer. If we exclude the cyclopropane ring,
the backbone structure of the dimer is planar. The hydrogen bond lengths in the best fit
structure became very asymmetric compared with the theoretical computation and the
separation of each of the monomers changes very little with the rotation angle φ. The
asymmetry of the hydrogen bonds in the “best fit” structure may confirm these steric
interactions of FA with the cyclopropane ring. A smaller asymmetry of the hydrogen
bond lengths was found for the more symmetric doubly hydrogen bonded complex
propiolic acid-formic acid and 1,2-cyclohexanedione-formic acid (next chapter).109
For the transitions measured of the CPCA – FA dimer, there appeared to be a
small splitting within each transition and an example of this splitting can be observed in
Figure 6.1.1. This is due to Doppler Effects commonly observed in spectra using PBFT
spectrometers and likely not due to proton tunneling as was observed in other
carboxylic acid dimers. The magnitude of the splitting increased with increasing
frequency of the transitions, typical of Doppler type splittings. To confirm that these
splittings were indeed Doppler splittings, a 50/50 argon/neon mixture was used as the
carrier gas and, as expected with the presence of argon, these Doppler splittings
decreased slightly. Tunneling splittings were not observed, most likely because the
136
dimer lacks the C2v(M) symmetry, which may be necessary to create the symmetric
double well potential, allowing for the protons to tunnel through the energy barrier.
Because this dimer lacked C2v(M) symmetry, the resulting potential energy surface is
more asymmetric, “locking” the dimer in the lower of the tunneling configurations. The
doubly hydrogen bonded dimers that exhibit this proton tunneling seem to have this
symmetry, or very close to it.
137
6.2 1,2-CYCLOHEXANEDIONE (MONOENOLIC) – FORMIC ACID DIMER
6.2.1 INTRODUCTION
There has been substantial interest in doubly and triply hydrogen-bonded
complexes since they provide simple models for the hydrogen bonding that exists
between the complementary base pairs in DNA. These hydrogen-bonded dimers are
not static structures and have been shown to exhibit proton tunneling dynamics in the
gas phase. There have been several doubly hydrogen-bonded dimers in which the
structure and proton tunneling have been studied. These dimers include complexes
such as propiolic acid - formic acid and acetic acid - formic acid. 1,2-cyclohexanedione
(1,2-CDO) exhibits tautomerization to the monoenolic form and this is the favorable
tautomer for forming a dimer with formic acid. This results in a dimer structure capable
of forming two hydrogen bonds similar the above dimers. Since 1,2-CDO is nonplanar,
the dimer with formic acid is a bit more complex than the hydrogen-bonded dimers listed
above and does not have a C2V(M) symmetry. Due to the lack of symmetry in this dimer,
the proton tunneling motion is not expected to be observed. Studying asymmetric
dimers is still important as a tunneling case without a symmetric double well potential
will be important to characterize and will be necessary to determine how asymmetric the
dimers can be to still exhibit the proton tunneling.
6.2.2 MICROWAVE MEASUREMENTS
The microwave spectrum was measured in the 4.5-9 GHz range for the hydrogen
bonded dimer between 1,2-cyclohexanedione (1,2-CDO) and formic acid (FA).
Measurements were made using a pulsed-beam Fourier transform (PBFT) microwave
138
spectrometer. Four isotopologues were measured, including the parent, a single
deuterium substitution at H12 on FA, a single deuterium substitution at H14 on 1,2CDO, and a double deuterium substitution at H12 and H14 on FA and 1,2-CDO
respectively. The atom numbering scheme is shown in Figure 6.2.1. There were 49
transitions measured in total; 19 for the parent isotopologue, 10 for the single deuterium
substitution at H12 on FA, 10 for the single deuterium substitution at H14 on 1,2-CDO,
and 10 for the double deuterium substitution at H12 on FA and H14 on 1,2-CDO. These
transitions are all listed in Tables 6.2.1-3.
Figure 6.2.1. Best fit structure of the 1,2-CDO and FA hydrogen-bonded dimer.
139
Table 6.2.1 Results of the measurements and least squares fit calculations for 1,2CDO/FA parent dimer isotopologue transitions. The standard deviation of the fit is 0.002
MHz. Frequencies are given in MHz.
J′Ka’Kc’
515
505
524
523
514
616
606
625
624
615
717
707
726
725
716
818
808
827
909
J″Ka”Kc”
414
404
423
423
413
515
505
524
523
514
616
606
625
624
615
717
707
726
808
obs
o-c
4732.9860
4911.8100
4969.4110
5034.3650
5191.5510
5671.5780
5860.6920
5957.2310
6068.6140
6219.5780
6606.4180
6794.6320
6941.7680
7114.4330
7241.2990
7537.3440
7714.6800
7922.5080
8623.3360
-0.002
-0.002
-0.001
0.001
0.002
-0.001
0.000
-0.000
0.001
0.002
0.002
-0.001
0.001
-0.003
-0.001
0.002
0.001
0.000
-0.001
Table 6.2.2 Results of the measurements and least squares fit calculations for 1,2CDO/DFA parent dimer isotopologue transitions. The standard deviation of the fit is
0.003 MHz. Frequencies are given in MHz.
J′Ka’Kc’
413
515
505
524
514
616
606
615
707
808
J″Ka”Kc”
312
414
404
423
413
515
505
514
606
707
obs
o-c
4064.9410
4635.9410
4809.4060
4862.0070
5075.0680
5555.7840
5740.5340
6080.7580
6657.6900
7561.5940
0.002
0.001
-0.000
-0.000
0.001
-0.000
-0.001
-0.002
-0.001
0.001
140
Table 6.2.3 Results of the measurements and least squares fit calculations for 1,2DCDO/FA and 1,2-DCDO/DFA dimer isotopologue transitions. Frequencies are given in
MHz. The standard deviation of the fits are 0.003 MHz and 0.002 MHz respectively.
1,2-DCDO/FA
J′Ka’Kc’
515
505
616
606
717
707
818
808
919
909
J″Ka”Kc”
414
404
515
505
616
606
717
707
818
808
obs
o-c
4723.0850
4901.9722
5659.5898
5848.4570
6592.3052
6779.8853
7521.0698
7697.3687
8445.8906
8603.4980
-0.002
0.004
-0.004
-0.001
-0.001
-0.001
0.002
0.000
0.004
-0.000
1,2-DCDO/DFA
obs
o-c
4626.7041
4800.2813
5544.6025
5729.1812
6458.9888
6643.9844
7369.7031
7545.4683
8276.7246
8435.7979
-0.001
0.002
-0.001
0.000
-0.003
-0.001
-0.001
-0.002
0.004
0.001
The 1,2-CDO (97%) and FA (98%) samples were purchased from Sigma Aldrich
and were used without further purification. The deuterated FA was purchased from CDN
isotopes (99.2% D) and was also used without further purification. The deuterated 1,2CDO sample was prepared by mixing equimolar quantities of 1,2-CDO (Sigma Aldrich,
97%) and MeOD (Cambridge Isotope Lab, Inc., 99%) and letting them exchange
overnight. The remaining MeOH was removed from the mixture under reduced pressure
and the deuterated 1,2-CDO crystallized in the flask and was then removed and
transferred to a small vial to be used for the measurements.
The samples of 1,2-CDO and FA were transferred into separate glass sample
cells. The cell containing 1,2-CDO was attached to the pulsed-valve (General Valve
series 9) and was heated to ~35 °C. The cell containing FA was placed in the neon gas
line leading to the cell containing 1,2-CDO. The FA sample was maintained at -10 °C
141
using a Peltier cooling system. The pressure inside the spectrometer was maintained at
10-6 to 10-7 Torr prior to the pulsed injection of the samples and the Ne carrier gas,
which was maintained at ~1 atm. The valve was set to pulse at ~2 Hz. A similar set up
was used to measure the transitions of all other isotoplogues, using the respective
isotopic samples of either the deuterated 1,2-CDO or FA. An example of an observed
transition is shown in Figure 6.2.2. Some small splittings of lines were observed but
none are assigned to possible proton tunneling. These splittings are a result of the
Doppler Effect, which is present in these pulsed beam experiments as was discussed in
the previous chapter. The present complex does not possess a C2 symmetry axis, so
we would expect an asymmetric tunneling potential making it unlikely that concerted
proton tunneling splittings would be observed.
Figure 6.2.2 Example of observed transition for 1,2-CDO – FA parent (505-606, 245
pulsed-beam cycles) at stimulating frequency 5860.900 MHz. The horizontal axis
represents the difference of the observed transition from the stimulating frequency,
shown in KHz.
142
6.2.3 CALCULATIONS
Ab initio computations to obtain an optimized equilibrium structure were
performed using Gaussian 09 suite using MP2 with a 6-311++G** basis set in order to
obtain initial values of the rotational constants. The rotational constants from the
optimized Gaussian structure were used to predict the a-dipole rotational transitions as
the a-dipole moment component was predicted to be the largest leading to stronger
transitions. The optimized values of the rotational constants were A=2413.722 MHz,
B=544.074 MHz, and C=454.138 MHz. These calculated rotational constants fall within
0.6% of the experimental values, limiting the scan range of the experiment and aided in
quantum number assignments of the rotational states involved in the measured
transitions. A comparison of the hydrogen bond distances and the center of mass
separations of the calculated Gaussian and experimental structure are shown in Table
6.2.4.
Table 6.2.4
Interatomic distances obtained by fitting the experimental rotational
constants for four isotopologues. Hydrogen bond lengths and COM separations are in
Å.
Interatomic Distance Microwave Fit Value
(Å)
r(H13-O8)
1.973(30)
r(H14-O11)
1.975(30)
COM Separation
4.591(2)
143
Calculated
Value (Å)
1.771
1.886
4.571
6.2.4 ROTATIONAL CONSTANTS
Experimental rotational and centrifugal distortion constants for the parent
isotopologue of the dimer were determined using a nonlinear least-squares fitting
program and are given in Table 6.2.5. A similar analysis was carried out for the
remaining 3 isotopologues of the dimer, but the centrifugal distortion constants were
held fixed to the values obtained from the parent isotopologue. The observed (o) and
calculated (c) rotational transition frequencies from the fit rotational constants for each
of the isotopologues are given in Tables 6.2.1-3.
Table 6.2.5
Atom Cartesian coordinates in a, b, c system for the best fit structure of
1,2-CDO/FA hydrogen bonded dimer, and the Kraitchman determined values (Krait.) for
the isotopic substitutions.
Atom
C1
C2
C3
C4
C5
C6
C7
O8
O9
O10
O11
H12
H13
H14
H15
H16
H17
H18
H19
H20
H21
a
2.236
1.676
3.383
0.946
2.981
0.582
-3.616
-0.608
-0.089
-3.374
-2.840
-4.631
-2.459
-0.884
2.448
1.832
1.341
4.245
3.707
2.817
3.782
b
0.100
0.257
0.124
0.037
-0.394
0.031
0.001
-0.031
-0.103
-0.001
0.000
0.006
0.014
-0.094
0.075
1.344
-0.088
-0.436
1.173
-1.477
-0.221
c
1.290
-1.554
0.308
0.887
-1.074
-0.543
0.165
-0.846
1.753
-1.240
0.943
0.550
-1.527
1.195
2.357
-1.616
-2.536
0.687
0.227
-1.013
-1.800
144
|a| -Krait.
|b| -Krait.
|c| -Krait.
4.7(8)
0.06(1)
0.15(3)
1.(1)
0.03(2)
1.(1)
6.2.5 MOLECULAR STRUCTURE
The rotational constants acquired from each of the microwave fits of the
isotopologues were used in a nonlinear least squares fitting program to determine the
experimental hydrogen bond lengths and the center of mass separation of the 1,2-CDO
and FA monomers. In the fit, 1,2-CDO coordinates were held fixed to those obtained
previously.110 Structural parameters for formic acid were obtained from the work of
Gerry108 and were also held fixed. The coordinates of both monomers were initially set
up in such a way that the sp2 hybridized carbon atoms of 1,2-CDO (C1, C4, and C6) and
FA (C7), as well as all oxygen atoms and the hydrogen atoms H12-15, were in the
same plane (the x-y plane). There were two variable parameters assigned during the
structure fit. These parameters represented the x - y coordinates for the center of mass
of FA, with respect to the coordinate system of 1,2-CDO. A third fixed parameter, 
(phi), represented the rotation of the formic acid moiety in the x-y plane. The rotation of
the FA moiety was held fixed to = -0.1047 radians, as this angle produced the best
structure with the smallest deviation of its calculated rotational constants compared with
the experimentally determined values obtained from assigning the transitions. The value
of the angle  is not as important as the hydrogen bond lengths that result and the COM
separation changes very little with . The center of mass separation of the monomers
was calculated using the parallel axis theorem resulting in the equation ICC = ICC(1,2CDO) + ICC(FA) + µR2CM. The calculated and experimental values for the hydrogen bond
lengths and the center of mass separations are shown in Table 6.2.4.
The experimental A, B, and C rotational constants and the deviations from the
best fit calculated values are listed in Table 6.2.6. Values of the atomic coordinates
145
obtained from the structure fit are shown in Table 6.2.5. Coordinates for the substituted
atoms were also obtained by performing a Kraitchman analysis. We do not believe that
all of the magnitudes of coordinates from the Kraitchman analysis are very accurate nor
reliable due to the substitutions being in close proximity to the principal axes or center of
mass of the dimer, but they are all included in Table 6.2.5 for reference.
Table 6.2.6
MEASURED rotational constants and the “best fit” CALCULATED values
for rotational constants obtained from the structure fit. The standard deviation for the fit
is 1.12 MHz. Also shown are the distortion constants (kHz) of the parent isotopologue,
held fixed for all other isotopic substitutions.
ISOTOPOLOGUE
Parent
A
B
C
DJ
DJK
CDO-DFA
A
B
C
DCDO-FA
A
B
C
DCDO-DFA
A
B
C
MEASURED
2415.0439(179)
543.6907(2)
451.6663(2)
0.0220(13)
0.119(31)
2414.7543(379)
530.9216(2)
442.8253(3)
2399.6875(257)
542.9527(9)
450.6175(3)
2399.4147(226)
530.2502(7)
441.8415(2)
CALCULATED
2417.1848
543.7113
450.8779
(M. – C.)
-2.1410
-0.0206
0.7884
2413.7931
531.4466
442.2975
2400.6990
543.2486
449.9907
2397.5249
531.0291
441.4666
0.9613
-0.5250
0.5278
-1.0115
-0.2959
0.6267
1.8897
-0.7789
0.3749
6.2.6 DISCUSSION
The pure rotational spectrum of the doubly hydrogen bonded dimer of 1,2cyclohexanedione and formic acid has been measured using a PBFT microwave
spectrometer and all measured rotational transitions were assigned. The experimental
146
rotational transitions are shown in Tables 6.2.1-3 and the best fit hydrogen bond lengths
and center of mass separations and structural coordinates of the dimer are given in
Tables 6.2.4 and 6.2.5 respectively. The best fit structure shown in Figure 6.2.1
produced more symmetric and slightly longer hydrogen bond lengths when compared
with the Gaussian calculation. The experimental hydrogen bond lengths of 1.97 Å are a
bit longer than the optimized (Gaussian) values of 1.77 Å and 1.89 Å. This difference is
a bit larger than expected, but in the correct direction since the experimental values are
r0 and calculated values are for re. We believe that the average of the hydrogen-bond
lengths is quite accurate (rOH = 1.97(1)) but the uncertainty is perhaps a factor of 2 or 3
higher for the individual hydrogen bond lengths (rOH = 1.97(3)) because the fit was not
very sensitive to the angle . More isotopologue transitions need to be measured to
determine a more complete and accurate gas phase structure for this dimer.
147
6.3 MALEIMIDE – FORMIC ACID DIMER
6.3.1 INTRODUCTION
Interest to study hydrogen bonded complexes has been growing over recent
years to better understand these interactions. Hydrogen bonded systems are prevalent
all throughout nature and can be seen in systems such as DNA, with the hydrogen
bonding between base pairs, or in proteins as the secondary structure is highly
dependent upon the amount of hydrogen bonding present. Hydrogen bonding
interactions give rise to proton tunneling motions, and some of these tunneling motions
may be associated with point mutations in DNA that may cause disease. In the gas
phase, some of these hydrogen bonded dimers formed between two carboxylic acids
have been shown to exhibit this proton tunneling motion. Information about the
dynamics of this tunneling motion, such as the tunneling splitting, can be determined
directly through the analysis of the microwave spectra. Further analysis of the structure
and the tunneling splitting can yield information about the potential energy surface
specifically the barrier height between the two tunneling configurations. Studying these
systems is important to better understand these types of phenomena and provide
benchmarks to help improve the accuracy of theoretical computations for larger
systems.
Previously studied doubly hydrogen bonded carboxylic acid dimers that exhibited
the tunneling motion maintained a C2v(M) symmetry, allowing for a symmetric potential
energy surface. One of these dimers is the propiolic acid – formic acid dimer. The
double hydrogen bonded dimer formed between the monoenolic tautomer of 1,2cyclohexanedione and formic acid (CDO-FA), discussed in the previous section, had
148
low symmetry and was not a dimer formed between two carboxylic acids; no proton
tunneling was observed. In this study, the maleimide – formic acid (Mal-FA) doubly
hydrogen bonded dimer, which also does not have C2v(M) symmetry, was observed. It is
important to study even the asymmetric hydrogen bonded dimers because if the
tunneling motion is observed, then the C2v(M) symmetry thought to be required may not
be necessary to observe this tunneling effect. Furthermore, it will be important to
characterize the tunneling splitting in dimers without a symmetric potential energy
surface and answer an important question about how asymmetric can the dimers be
and the tunneling still be present. Many of the dimers studied are formed between
carboxylic acids or other similar oxygen containing species, as in the CDO-FA dimer,
but it is important to also characterize the dimers with nitrogen containing groups, as
there may be structural differences when compared to the complexes with the oxygen
containing species.
6.3.2 CALCULATIONS, MICROWAVE MEASUREMENTS, AND DATA ANALYSIS
DFT computations were performed on the Mal-FA dimer in order to obtain
preliminary rotational constants and quadrupole coupling strengths for this system,
allowing for the pure rotational transitions to be predicted using Pickett’s SPCAT
program. A B3LYP method was used with an aug-cc-pVTZ basis using the Gaussian 09
suite on the HPC system at the University of Arizona. Additional predictive calculations
were performed to predict the rotational constants of the deuterated isotopologues.
These were performed by first determining the ratio, or scale factor, between the parent
experimental and calculated rotational constants. The scale factor was then multiplied
149
by the calculated rotational constants of the deuterated isotopologue, which were
recalculated using Kisiel’s PMIFST program,111 after changing the mass of the
respective substituted H atom. Usually these corrected values of the rotational
constants for the singly substituted isotopologues are very close to experimental values
for 13C substituted isotopologues. In the case of these D substituted isotopologues, the
H atoms are distant from the principle axes, thus making the effect of changing the
mass of H to D larger, resulting in predicted rotational constants that did not agree very
well with the fit experimental values and so some searching was required to observe
and measure these D substituted rotational transitions.
The rotational transitions were measured for the parent in the 4.9 – 10 GHz
range using a Flygare-Balle type pulsed-beam Fourier transform microwave
spectrometer that has been previously described. The maleimide sample was
purchased from Sigma Aldrich (99%) and was used without further purification. The
pressure inside the vacuum cavity was maintained at 10-6 to 10-7 Torr prior to the pulse
of the molecular beam. The backing pressure of the Ne carrier gas was maintained at ~
1 atm. In order to obtain sufficient vapor pressure of the maleimide sample, the sample
cell and pulsed valve were heated to ~70 °C. To prepare the doubly hydrogen bonded
dimer, the maleimide and formic acid samples were transferred to separate glass
sample cells. Within the Ne gas line, the cooled formic acid (-8 °C) sample cell was
placed before the maleimide sample cell and the temperature of the FA was maintained
using a Peltier cooling device. This allowed the FA vapor to be seeded into the Ne
carrier gas before picking up the gaseous maleimide sample. All measured rotational
transitions for the parent are shown in Table 6.3.1 and the transitions measured of each
150
of the D substituted isotopologues are shown in Table 6.3.2. There was no evidence of
the concerted proton tunneling motion as many b-type transitions were measured and
used in the fits. If proton tunneling is present, the b-type transitions will be significantly
split possibly by hundreds of MHz, due to these ro-vibrational transitions changing
vibrational states.
Table 6.3.1
Measured rotational transitions of the maleimide – formic acid
heterodimer and the differences (o-c) from the calculated values in the fit. Values shown
are in MHz.
J′ Ka’ Kc’ F’
2 2 0 2
4 1 4 5
4 1 4 4
3 1 3 4
3 1 3 3
4 0 4 5
4 0 4 4
4 2 3 3
4 2 3 5
4 2 3 4
5 0 5 5
5 0 5 6
5 0 5 4
4 1 3 3
4 1 3 5
4 1 3 4
3 2 2 3
3 2 2 4
5 1 5 6
5 1 5 5
5 0 5 4
5 0 5 5
5 2 4 5
5 2 4 6
5 2 4 4
5 2 4 6
5 2 4 5
J″ Ka” Kc” F”
2 1 1 2
3 1 3 4
3 1 3 3
2 0 2 3
2 0 2 2
3 0 3 4
3 0 3 3
3 2 2 2
3 2 2 4
3 2 2 3
4 1 4 4
4 1 4 5
4 1 4 3
3 1 2 2
3 1 2 4
3 1 2 3
3 1 3 3
3 1 3 4
4 1 4 5
4 1 4 4
4 0 4 3
4 0 4 4
5 1 5 5
5 1 5 6
5 1 5 4
4 2 3 5
4 2 3 4
151
obs
o-c
4907.953
5093.764
5093.864
5287.475
5288.088
5353.787
5353.961
5494.710
5494.768
5494.978
5632.969
5633.204
5633.323
5856.487
5856.553
5856.633
5764.425
5765.572
6342.525
6342.597
6593.400
6593.573
6671.616
6672.609
6672.816
6848.564
6848.697
0.006
0.002
-0.006
0.005
0.001
-0.004
0.003
0.002
0.006
0.006
-0.002
-0.004
-0.000
-0.002
0.005
0.001
-0.001
0.004
0.006
-0.008
-0.001
0.001
0.000
-0.003
0.001
-0.000
0.002
5
5
6
6
6
2
2
5
5
5
3
3
3
3
3
3
3
3
Table 6.3.2
3
3
1
0
0
2
2
3
3
3
2
2
2
2
2
2
2
2
3
3
6
6
6
1
1
2
2
2
2
2
2
2
2
1
1
1
6
5
6
7
6
3
2
5
5
6
4
2
3
3
2
3
4
2
4
4
5
5
5
1
1
5
5
5
2
2
2
2
2
2
2
2
3
3
1
0
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
5
5
5
0
0
3
3
3
1
1
1
1
1
2
2
2
5
4
5
6
5
2
1
4
6
6
3
3
3
2
2
2
3
1
6930.662
6930.853
7578.725
7793.394
7793.556
7837.498
7837.952
8267.066
8267.096
8267.188
9022.316
9022.316
9022.316
9022.830
9022.830
9676.429
9677.607
9678.211
-0.005
-0.001
0.001
0.005
-0.003
-0.004
-0.005
0.002
-0.008
0.007
-0.002
-0.002
-0.002
-0.009
-0.009
-0.001
0.007
0.001
Measured rotational transitions of the isotopologues of the Mal-FA dimer
and the differences (o-c) from the calculated values in the fit. Values shown are in MHz.
Rotational Transitions
J′ Ka’ Kc’ F’ J″ Ka” Kc” F”
2 2 0 1
2 1 1 1
2 2 0 3
2 1 1 3
4 1 4 5
3 1 3 4
4 1 4 4
3 1 3 3
3 1 3 2
2 0 2 1
3 1 3 4
2 0 2 3
3 1 3 3
2 0 2 2
4 0 4 5
3 0 3 4
4 0 4 4
3 0 3 3
5 0 5 5
4 1 4 4
5 0 5 6
4 1 4 5
5 0 5 4
4 1 4 3
4 1 3 3
3 1 2 2
4 1 3 5
3 1 2 4
4 1 3 4
3 1 2 3
5 1 5 6
4 1 4 5
5 1 5 4
4 1 4 3
5 0 5 6
4 0 4 5
5 0 5 4
4 0 4 3
Mal – (D)FA
obs
o-c
4926.610
4926.645
4984.640
4984.742
5217.600
5217.708
5218.325
5238.871
5239.036
5469.778
5470.032
5470.153
5717.417
5717.487
5717.567
6207.899
6207.954
-0.001
0.000
-0.006
-0.004
0.010
-0.001
0.001
-0.006
0.000
-0.002
-0.002
0.004
-0.007
0.004
0.008
0.002
0.009
6456.280
-0.007
152
Mal(ND) – FA
obs
5088.241
5088.347
5271.962
5272.074
o-c
-0.006
-0.002
0.001
-0.001
5348.165
5636.195
5636.430
5636.546
0.001
-0.005
-0.002
0.004
5853.249
5853.324
6335.367
6335.420
6585.264
0.002
0.000
0.000
0.006
-0.002
Mal – FA(OD)
obs
o-c
4897.0811
4897.1440
5055.5005
5055.6011
5256.7998
5256.9155
-0.003
0.005
-0.004
0.000
0.005
-0.003
5313.5459
5313.7095
5581.7734
5582.0132
5582.1284
5809.5996
5809.6655
-0.007
-0.003
0.004
0.001
0.006
-0.006
0.001
6295.1514
0.002
6544.7793
-0.006
5
6
6
6
6
6
6
0
1
1
1
0
0
0
5
6
6
6
6
6
6
5
7
5
6
5
7
6
4
5
5
5
5
5
5
0
1
1
1
0
0
0
4
5
5
5
5
5
5
4
6
4
5
4
6
5
6456.449
-0.004
7419.320
7419.359
7635.267
7635.267
7635.427
0.003
0.004
-0.004
0.002
-0.004
6585.437
7569.764
7569.798
7569.839
7782.922
-0.002
0.003
0.005
0.006
0.004
6544.9556
7522.3765
0.004
0.009
7522.4468
7736.7603
0.011
-0.003
7783.064
-0.014
7736.9170
-0.005
The experimental rotational, quadrupole coupling (for 14N) and centrifugal
distortion constants were determined from the assigned rotational transitions for each of
the isotopologues using Pickett’s SPFIT program and these values are shown in Table
6.3.3. The quadrupole coupling strengths of D were not determined for those
isotopologues with a D substitution as the D hyperfine structure was not resolved. The
calculated values are within 0.1% of the experimental values. During the microwave fits
for the isotopologues, the centrifugal distortion constants were held fixed to the values
obtained from the parent. The experimental inertial defect was ∆ = -0.528 amu Å2,
indicating the molecular structure is planar with a value close to zero. The small
negative nonzero value of this inertial defect indicates the presence of out of plane
vibrational motions within this dimer. Compared with the inertial defect of the maleimide
monomer (∆ = -0.0536 amu Å2),112 the magnitude of the inertial defect of the dimer is
larger, suggesting more out of plane vibrational modes.
153
Table 6.3.3
Fit rotational, centrifugal distortion, and quadrupole coupling constants of
the Mal – FA dimer. Also shown is the B3LYP/aug-cc-pVTZ calculated values.
A/MHz
B/MHz
C/MHZ
1.5χaa/MHz
0.25(χbb- χcc)/MHz
DJ/kHz
DJK/kHz
DK/kHz
N
σ/kHz
Parent
2415.0297(11)
784.37494(41)
592.44190(36)
2.083(15)
1.1565(32)
0.0616(69)
-0.118(38)
-1.38(16)
45
4
B3LYP/aug
-cc-pVTZ
2414.7720
784.34024
592.04019
2.150
1.1865
-ND
2403.7960(43)
784.16342(70)
591.65013(28)
1.86(11)
1.118(17)
0.0616*
-0.118*
-1.38*
19
5
D-FA
2402.0396(22)
764.72770(54)
580.42763(25)
1.860(44)
1.136(10)
0.0616*
-0.118*
-1.38*
24
5
FA-OD
2405.0404(22)
777.87629(55)
588.13551(25)
1.694(40)
1.117(12)
0.0616*
-0.118*
-1.38*
20
5
* Centrifugal distortion constants were held fixed to the experimental parent isotopologue values during the microwave fits of each
isotopologue.
From the rotational constants of the parent and each D substituted isotopologue,
a nonlinear least squares fit was performed to determine the best fit gas phase structure
of this hydrogen bonded dimer. This fitting program varies the Cartesian coordinates of
the atoms within the molecules to obtain a structure that calculates rotational constants
closest to the experimentally determined values obtained from assigning the measured
transitions to the correct energy levels. During the fit, the atomic coordinates of Mal
were held fixed to previously obtained values (discussed earlier in this dissertation) and
the structure of formic acid was held fixed to what was obtained from the work of
Gerry.108 Because the structure of the Mal monomer is an averaged structure of both
equilibrium and ground state atomic coordinates, the obtained structure of the dimer is
also a vibrationally averaged structure. We believe the differences in these structures
are small and this best fit structure reasonably represents this dimer in the ground state.
There were 2 varied parameters during the structure fit which varied the coordinates of
154
FA in the molecular (a-b) plane. A third parameter, φ, was the rotation of the formic acid
coordinates within this molecular plane. φ was not varied, but was set to a value that
provided the smallest standard deviation in the structure fit, which was 1.09 MHz. This
best fit structure can be seen in Figure 6.3.1 and the hydrogen bond lengths from the
B3LYP calculation and the best fit structure are compared in Table 6.3.4. The best fit
structure seemed to correlate with the formic acid moiety slightly rotated to increase the
length of r(H6-O13) and decrease the length of r(O12-H10). The center of mass
separation, determined through the use of the parallel axis theorem, of the monomer
units remained unchanged from the calculation and the experimentally determined
rotational constants.
Figure 6.3.1 Best fit structure of the maleimide – formic acid dimer, showing the
hydrogen bond distances in Å.
155
Table 6.3.4
Hydrogen bond distances and center of mass separation of the
monomers in the best fit structure compared with the B3LYP/aug-cc-pVTZ calculated
values, shown in Å.
Interatomic Distance Microwave Fit Value
r(H6-O13)
r(O12-H10)
COM Separation
2.027
1.634
4.06
Calculated
(B3LYP) Value
1.874
1.685
4.06
The principle axes coordinates of the best fit structure are shown in Table 6.3.5
along with the Kraitchman determined coordinates for the single D substituted H atoms,
which were calculated using Kisiel’s KRA program. The Kraitchman determined
coordinates only give the magnitudes and so the absolute values of the coordinates are
shown. The D substituted coordinates do not agree very well with the best fit structure,
indicating a large change of the molecular structure upon the isotopic substitution. The
change in structure upon substitution agrees with the fact that the rotational constants of
these D isotopologues could not be predicted very accurately by changing the mass of
each of these substituted atoms. Since the nonlinear least squares fitting program
assumes the structure does not change upon isotopic substitution, this current structure
can be refined with the measurement of transitions from singly substituted 13C and 15N
isotopologues to obtain more accurate hydrogen bond distances.
156
Table 6.3.5
Best fit atomic coordinates (Å) of the best fit structure compared with the
Kraitchman determined coordinates of the substituted D isotopes. The Kraitchman
values only show the magnitudes of the COM coordinates.
Atom
C1
C2
C3
C4
C5
H6
H7
H8
H9
H10
O11
O12
O13
O14
N15
a
0.469
1.868
2.726
1.908
-3.095
-0.200
2.091
3.808
-4.143
-2.005
2.313
-0.564
-2.184
-2.958
0.586
b
-1.006
-1.542
-0.481
0.775
0.642
1.007
-2.601
-0.477
0.944
-0.871
1.918
-1.642
1.425
-0.691
0.371
Krait-|a|
Krait-|b|
0.4042(38)
0.9895(15)
4.06138(38)
2.31736(66)
1.0843(14)
0.9384(16)
6.3.3 CONCLUSIONS
Rotational transitions were measured for the maleimide – formic acid doubly
hydrogen bonded dimer and three single D substituted isotopologues. There was no
evidence of the double concerted proton tunneling in the measurement of the rotational
transitions of this dimer, further suggesting that C2v(M) symmetry is required to observe
this tunneling effect. The best fit gas phase structure is an averaged structure of
equilibrium and ground state atomic coordinates, but is a reasonable representation of
the ground state of this dimer. The current structure can be further refined with the
measurement of additional isotopologue transitions.
157
6.4 TROPOLONE – FORMIC ACID DIMER
6.4.1 INTRODUCTION
Tropolone, or 2-hydroxy-2,4,6-cycloheptatriene-1-one, is a seven membered ring
and a pseudoaromatic molecule.113 The carbonyl and hydroxyl groups interact with each
other to form a stabilizing intramolecular hydrogen bond. Tropolone has been previously
studied and it was observed that the hydrogen atom on the hydroxyl group tunnels
between the two oxygen atoms in the molecule. The structure after tunneling occurs is
identical to the configuration before the tunneling motion. The tunneling motion is
described by a symmetric potential energy surface that has a double well minima that is
caused by the C2v(M) symmetry along the proton tunneling coordinates. The proton
tunneling effect has been extensively studied for other systems using microwave
spectroscopy, rotationally resolved degenerate four-wave mixing,114,115,116,117,118 matrixisolated infrared spectroscopy,119,120 laser-induced fluorescence (LIF) techniques,121,122
and gaseous infrared spectroscopy.123,124,125,126
The magnitude of the splitting between ro-vibrational transitions can be affected
by a number of factors. Some of these factors are the motion of the tunneling proton,
displacement of nuclei during the tunneling motion, redistribution of electronic charge,
energy and mode of the vibrational excitation, and asymmetric isotopic substitutions.
The barrier height can also be influenced by intermolecular interactions, such as the van
der Waals complexes formed with noble gases or hydrogen bonding.127 Previous
microwave studies reported the microwave spectrum of Ar-tropolone and H2O-tropolone
and found that the weak interactions both quench the proton tunneling motion.128,129
158
There also may have been other interactions with H2O that may have quenched the
tunneling.
Formic Acid is known to form doubly hydrogen bonded dimers with several
carboxylic acids. Some of these dimers exhibit proton tunneling and some do not. The
microwave spectra of cyclopropanecarboxylic acid – formic acid (CPCA-FA) dimer was
previously discussed in chapter 6.1 and no tunneling was observed for this doubly
hydrogen bonded dimer, due to its lack of symmetry. Due to the tropolone-formic acid
doubly hydrogen bonded dimer possessing the C2V(M) symmetry, the potential energy
surface has a symmetric double well potential and the proton tunneling motion is
expected to be observed in this study. An image of this dimer is shown below in Figure
6.4.1.
Figure 6.4.1 Calculated B3LYP/aug-cc-pVTZ structure of the Tropolone – Formic Acid
doubly hydrogen bonded dimer. Hydrogen bond lengths are shown in Å.
159
6.4.2 MICROWAVE MEASUREMENTS
The microwave spectrum was measured for the tropolone – formic acid doubly
hydrogen bonded dimer in the 4.7 – 9 GHz range and all assigned transitions are shown
in Table 6.4.1.
Table 6.4.1
Measured a- and b-type rotational transitions of the tropolone – formic
acid doubly hydrogen bonded dimer. Values are shown in MHz.
J′ Ka’ Kc’
4 14
6 16
6 06
6 33
6 24
5 15
7 17
7 07
7 35
7 34
6 16
7 25
7 16
8 18
8 08
7 17
8 17
9 19
8 18
9 09
9 19
10 0 10
10 1 9
11 1 11
11 0 11
J″ Ka” Kc”
3 03
5 15
5 05
5 32
5 23
4 04
6 16
6 06
6 34
6 33
5 05
6 24
6 15
7 17
7 07
6 06
7 16
8 18
7 07
8 08
8 08
9 09
9 18
10 1 10
10 0 10
obs
o-c
4776.994
4879.911
5051.614
5169.534
5237.764
5444.692
5683.893
5855.119
6030.552
6038.775
6089.936
6141.604
6257.955
6484.354
6646.059
6722.206
7133.512
7281.295
7351.443
7426.650
7986.682
8199.868
8856.853
8865.250
8968.743
0.006
-0.001
-0.002
0.000
0.000
-0.007
0.004
0.004
0.001
0.002
0.003
-0.005
0.001
0.001
-0.001
0.000
0.003
-0.003
-0.001
-0.002
-0.001
-0.003
-0.003
0.005
0.000
These measurements were taken using a Flygare-Balle type pulsed-beam
Fourier transform microwave spectrometer that has been previously described. The
160
tropolone (98%) and formic acid (98%) samples were both purchased from Sigma
Aldrich and used without further purification. The samples were transferred to separate
glass sample cells. The cell containing tropolone was placed in the Ne gas line just
before the pulsed valve (General Valve Series 9) and was set to pulse at room
temperature. The Ne backing pressure was maintained at about 1 atm. The tropolone
sample was pulsed until there was a strong parent test signal recorded. Once the
tropolone signal was sufficiently strong, the sample cell containing the formic acid was
placed in the Ne gas line, before the tropolone sample and the formic acid vapor was
passed over the tropolone sample with each molecular beam pulse. The sample of
formic acid was brought to -8 °C before attaching to the Ne gas line and this
temperature was maintained using a Peltier cooling device. The formic acid vapor was
pulsed over the solid tropolone sample for about 15 minutes, and then was removed
from the Ne gas line as this provided a sufficient concentration of formic acid to
measure the dimer transitions in a single pulsed beam cycle. The high concentration of
FA being pulsed into the cavity reduced the signal intensity of the dimer. The removal of
formic acid was also crucial to the experiment as tropolone is very hygroscopic and was
absorbing much of the water vapor within the formic acid sample.
6.4.3 CALCULATIONS AND ROTATIONAL CONSTANTS
DFT computations were performed on the HPC system at the University of
Arizona using the Gaussian 09 suite with a B3LYP method and a aug-cc-pVTZ basis.
The results from this calculation are shown in Table 6.4.2. The calculated rotational
constants were used in the Pickett SPCAT program to predict the rotational transitions
161
expected to be observed. The calculated dipole moment components were 3.8 D along
the a-axis and 0.6 D along the b-axis, so it was expected the a-type transitions would be
strongest and these were the transitions that were initially searched for. The rotational
and centrifugal distortion constants were determined from the 25 a- and b- type
rotational transitions using the Pickett SPFIT program and these determined parameters
are shown in Table 6.4.2 along with the calculated values.
Table 6.4.2
Experimental and calculated rotational constants of the tropolone – formic
acid doubly hydrogen bonded dimer.
A/MHz
B/MHz
C/MHZ
DJ/kHz
DJK/kHz
DK/kHz
N
σ/kHz
Parent
2180.7186(98)
470.87390(25)
387.68984(22)
0.0100(14)
0.102(28)
13.2(81)
25
3
B3LYP/augcc-pVTZ
2191.3931
474.39567
389.97457
6.4.4 DISCUSSION
The rotational spectrum was measured for the tropolone – formic acid doubly
hydrogen bonded dimer in the 4.7-9 GHz range using a pulsed-beam Fourier transform
microwave spectrometer. It was expected that this doubly hydrogen bonded dimer
would exhibit a concerted double proton tunneling motion as the dimer has a C2v(M)
symmetry resulting in a symmetric double well potential. This symmetry has been
suggested as a requirement to observe the proton tunneling motion in the gas phase
162
and it has been present in numerous other hydrogen bonded dimers exhibiting
observable tunneling splittings within the microwave spectra. When the doubly
hydrogen bonded dimer exhibits proton tunneling, each rotational transition measured is
split; the magnitude of this splitting ranges up to a few MHz for a-type transitions and
can be hundreds of MHz for b-type transitions and is dependent on the barrier height
and separation of the minima for the potential energy surface. When the splittings due
to tunneling are observed, a vibration-rotation coupling analysis is performed to fit the
spectra from the two tunneling states which are treated as two vibrational states. After
measuring both a- and b-type transitions for this dimer, no splittings for any transition
were observed indicating that this doubly hydrogen bonded dimer did not exhibit the
concerted double proton tunneling motion.
To get an estimate of the barrier height in the potential energy surface to the
transition state structure during the tunneling motion, the two tunneling protons were
held fixed between the tropolone and formic acid molecules such that the distance of
the proton between the two oxygens in each molecule was equivalent and a C2v
symmetry was maintained. The energy of this structure was calculated using
B3LYP/aug-cc-pVTZ and the difference in energy of the calculated equilibrium structure
and this predicted transition state structure was about 15000 cm-1. The distance that
each proton was estimated to move during the tunneling process is about 0.8 Å, which
is similar to what was found for the propiolic – formic acid dimer. The distance each
proton moves was found by taking the transition state O-H bond lengths and subtracting
the B3LYP optimized bond lengths and multiplying by 2 to get to the next tunneling
state. The large barrier height between the two tunneling states may be why the
163
concerted double proton tunneling motion was not resolved for this doubly hydrogen
bonded dimer as the estimated distance between the potential minima was similar to
propiolic acid – formic acid in which the proton tunneling process was observed in the
microwave spectra.
While measuring the rotational transitions from this dimer, the spectrum was
congested with numerous other transitions that had significant intensity. From the
optimization calculations, it was predicted that there are many low energy out of plane
vibrational modes. The inertial defect calculated from the experimentally determined
rotational constants is ∆ = -1.46 amu Å2. This is indicative of a planar structure with the
magnitude not being significantly large, but because of the nonzero negative value, this
is a confirmation that there is significant out of plane vibrational motion for this dimer.
After measuring many transitions and attempting to make sense and assign the
congested spectra, none of the additional transitions measured were able to be fit to an
excited vibrational state. The additional transitions are most likely from other complexes
formed with Formic Acid or water or a combination.
164
7. CONCLUDING REMARKS
Microwave spectroscopy is a very powerful technique that can be used to
determine accurate gas phase molecular structure parameters as well as additional
electronic structure information around nuclei that have a nuclear spin greater than one
half. The importance of the structure of molecules is very well known to all types of
chemists and this dissertation has studied and determined important structural
parameters for a wide variety of different organic molecules and hydrogen bonded
dimers. Not only are the determined structures in this dissertation important to
understand the fundamental chemistry in certain systems, but these structures also
supply theoretical chemists with excellent benchmarks on which to refine the theoretical
models. Today in chemistry, all sub-disciplines within the field are relying more on the
calculations to advance the research and understanding of chemical systems, so it is
very critical to have theoretical models which accurately describe, for instance the
hydrogen bonding in large systems such as in DNA or proteins and predict the quantum
mechanical effects such as proton tunneling or other large amplitude motions that may
occur. Even though the molecules discussed in this dissertation are considered small on
most standards, the available theory still only does a fair job in accurately predicting the
experimental spectra and molecular structure for the systems studied. The importance
to refine theoretical models based on benchmarks of larger molecules, such as the ones
discussed in this dissertation, is increasing to advance the understanding of chemical
systems.
Chapter four focused on what is considered large molecules in the microwave
spectroscopists’ realm. These are cyclopropanecarboxylic acid and 1,2-
165
cyclohexanedione. Both of these molecules undergo some transformation to produce a
new structure – cyclopropanecarboxylic acid is able to rotate the carboxylic acid group
around the single bond with the cyclopropane ring, producing a high energy conformer
which was observed and reported. In the case of 1,2-cyclohexanedione, the parent
dione molecule was unable to be observed and it appeared that there was a complete
tautomerization that occurred very readily under the experimental conditions to produce
its monoenolic form, which was then studied further in a doubly hydrogen bonded dimer
with formic acid, discussed in chapter 6. These two molecules provide great
benchmarks for theoretical chemists and these microwave studies also provide some
insight into the molecular dynamics within these molecules. Future work to study large
molecules will depend on an efficient method to bring the samples into the gas phase,
such as a laser ablation system. As these organic molecules become larger, the larger
number intermolecular interactions decreases the vapor pressure and so the laser
ablation source must be developed and implemented in the lab to study larger and more
biologically relevant organic systems.
Much of the time, molecules may look very similar but produce very different
microwave spectra. In the case of some molecules, if there is an atom that has a
nuclear spin greater than one half, this produces a quadrupole moment around that
nuclei which results in hyperfine interactions that give rise to the hyperfine structure
within the microwave spectra. The analysis of the hyperfine structure is possible by
measuring the high resolution microwave spectra obtained from the pulsed beam
experiments used in this dissertation. This splitting caused by the electric quadrupole
interactions within the molecules allows for additional electronic structure information to
166
be determined about the systems studied, directly providing details about the electric
fields in these molecules. Chapter 5 studied a couple of molecules related to a number
of different biochemical applications – maleimide and phthalimide. 4a,8aazaboranaphthalene was also discussed in chapter 5 and because this molecule has
two quadrupolar nuclei, there were increased splittings, providing a very rich spectrum
with a nice hyperfine structure. From this analysis, the extent of the aromatic character
was determined for this BN substituted naphthalene molecule by determining valence porbital occupations using a Townes-Dailey analysis. It was found that this molecule
displays similar aromatic character when compared to other N-containing aromatic
molecules, such as pyrrole. Future work on these BN substituted systems is important
so this class of molecules can be characterized and implemented in chemical
applications, such as hydrogen storage or other organic electronic devices such as
LEDs. One such system that will need to be studied is the BN-cyclohexane molecule,
which readily lost H2 to produce a BN-cyclohexene molecule, a nice example of the
hydrogen storage capabilities of such systems.
The pulsed-beam microwave technique utilized for all of the systems discussed
in this dissertation lends itself as a great method to produce hydrogen bonded
complexes that can be observed in the microwave spectrometer. Many hydrogen
bonded complexes (dimer, trimers, etc.) are readily produced in the pulsed-beam and
chapter 6 focused on the microwave spectra of doubly hydrogen bonded dimers. It has
been shown in previous research that there is a concerted double proton tunneling
motion between two molecules that make up a heterodimer if there is a C2V(M)
symmetry with respect to the principal axes; this symmetry creates a symmetric double-
167
well potential that allows for the tunneling motion to be resolved. A couple of the central
questions about these doubly hydrogen bonded dimers are: can the tunneling motion
and splitting caused by this tunneling be observed in heterodimers that do not have the
C2V(M) symmetry? How asymmetric can the dimers be and proton tunneling still be
observed? Cyclopropanecarboxylic acid – formic acid, the monoenolic tautomer of 1,2cyclohexanedione – formic acid, maleiminde – formic acid, and tropolone – formic acid
were all studied and detailed in this dissertation. The first three dimers do not have the
C2V(M) symmetry and no tunneling was observed in any of these dimers. It would be an
extremely important result if splitting caused from this tunneling motion was observed
for these asymmetric dimers as this has yet to be observed in such systems. The last
dimer, formed with tropolone, does have the C2V(M) symmetry about the a-principal
axis, but splitting caused from the proton tunneling motion was not observed. This may
have been due to a large barrier height in its potential energy surface as suggested by
the calculations performed for this dimer, making the tunneling splitting very small and
unable to be resolved in the spectra. The inertial defect calculated from the
experimental parameters also indicated significant out of plane vibrations for the dimer,
which may also quench the tunneling motion. Future work on hydrogen bonded
complexes should be extended to larger systems containing more than two hydrogen
bonds, additional dimers that exhibit the concerted proton tunneling (dimers with C2V(M)
symmetry), as well as organometallic doubly hydrogen bonded systems to observe the
effects metal centers have on the structure of hydrogen bonding. Optimization
calculations have been performed for the ferrocenecarboxylic acid – formic acid dimer
(Fc-COOH – FA) and these optimized rotational constants are listed below in Table 7.1.
168
This will be the first hydrogen bonded dimer studied with an organometallic complex.
Although this dimer is not expected to exhibit any proton tunneling due to its lack of
C2v(M) molecular symmetry, the large size and the effect of the metal center on the
structure will be useful to use as a benchmark to advance theoretical computations, as
the theoretical methods are less accurate for these organometallic systems. Additional
systems which could be studied include other hydrogen bonded dimers that have the
potential to exhibit proton tunneling (possessing the C2v(M) symmetry): propiolic acid –
nitric acid (PA – NA), benzoic acid – nitric acid (BzA – NA), and dimers with
phenylpropiolic acid and formic (PPA – FA), propiolic acid (PPA – PA), or nitric acid
(PPA – NA). The optimized rotational constants of these dimers are listed in Table 7.1.
Table 7.1. Optimized rotational constants for several doubly hydrogen bonded dimers
using B3LYP/aug-cc-pVTZ.
Dimer
A /MHz
B /MHz
C /MHz
Fc-COOH – FA
893.465
253.520
233.789
PA – NA
6084.953
643.850
582.243
BzA – NA
2938.885
293.324
266.704
PPA – FA
2915.683
193.343
181.319
PPA – PA
2913.863
132.097
126.368
PPA – NA
2903.485
153.218
145.538
Many molecules and dimers were studied and discussed throughout this
dissertation, but there is still much work to be done to advance research in the lab. A
169
laser ablation beam source needs to be constructed to allow for efficient vaporization of
extremely low vapor pressure samples, such as organic molecules that have
pharmaceutical implications or highly reactive, short-lived organometallic intermediates
which can only be synthesized in the gas phase using ablation techniques. The ablation
source will open the door for molecules that could not be put into the gas phase by the
traditional method of heating the solenoid pulsed valve. Laser ablation could also be
used to synthesize transient organometallic species, such as iron or chromium
carbonyls with ligands such as butadiene, H2 or N2. Furthermore, the technique of
chirped pulse microwave spectroscopy130,131 will also be another invaluable tool in the
lab to aid in the study of these complex molecules. Data from a large range of
frequencies can be collected in a fraction of the time it takes the traditional pulsed beam
spectrometer to scan the same range. Chirped pulsed microwave spectroscopy will
allow strong rotational transitions to be found very quickly and the pulsed beam setup
can be used to narrow in on the transitions to resolve the hyperfine splittings, allowing
for more efficient use of the spectrometers and lab resources. Additionally, the chirped
pulse microwave technique can also be used to probe chemical kinetics and
dynamics,132,133 opening the door for even more studies using microwave spectroscopy.
170
8. APPENDIX A
The following inputs are the examples of the formatted files needed to perform
the least squares structure fitting routine, written in the programming language Fortran.
The first file that follows is the input file, which introduces the rotational constants from
each of the unique singly substituted isotopologues. The first line in this input file is the
title, which can be anything the operator chooses. The following line is the indication of
the number of varied parameters, rotational constants, and iterations the program is set
to cycle through. The following line contains the initial values of the variable parameters
used in the structure fitting routine. These variable parameters are set and allow the
Cartesian coordinates of the molecule to be varied, which will provide a structure that
calculates rotational constants closest to all of the experimentally determined values.
The second file following the input file is the file in which all the atomic masses
and Cartesian coordinates are specified for the molecule or complex. This is the
subroutine that cycles through the data, which are the sets of rotational constants
determined for each of the isotopologues, and allows the designated coordinates to vary
by the variable parameters assigned to the coordinates of the atoms. Following the
adjustment of the coordinates within the structure, the rotational constants are
calculated from the resulting structure and compared with the constants designated in
the first file that were determined from the experimental spectra. The program will
continue until the sum of squares for the data has the smallest value. The Cartesian
coordinates and parameters are listed at the end of this file.
The final file is the output displaying the results of the sum of least squares fitting
routine. The input file is reiterated and displayed in this file and the values of the varied
171
parameters in the structure fit are listed for each subsequent iteration of the program. At
the end of the file are the final values of the varied parameters as well as all of the
calculated rotational constants of the resulting best fit structure (lowest sum of squares),
a comparison with the experimentally determined values listed in the input file (first file),
and the differences between the values. The final values of the varied parameters must
have errors smaller than the magnitudes of the parameters themselves, which indicates
that these parameters have been determined. The second file and two additional
Fortran programs (one is the main fitting program calling upon each subroutine and the
other calculates rotational constants), which are not shown here, are compiled using
g77 or a similar compiler which produces an executable for the specified information
within the modified files. The program is initiated via UNIX commands using the
standard input and output operators.
--------------------------------------------------------------------------------------------------------------------1,2-CDO FA DIMER
cdo-str1
2 12 1 18
0.0001, 0.0001, 0.0001
2415.043869 0
543.6907091 0
451.6663339 0
2414.754335 0
530.9215857 0
442.8252644 0
2399.687491 0
542.9527044 0
450.6174626 0
2399.414692 0
530.2501681 0
441.8414584 0
0
0
1
172
0
0
0
0
0
0
--------------------------------------------------------------------------------------------------------------------INPUT
C STRUCTURE FIT - BZZ1 - GSUB - ftbz7.f
C ** NEW FCNDP FOR
C LINK - FTHCO, FITB1, ROTSUB, CFAC
SUBROUTINE FCNDP(NP,ND,NV,NDATA,X1,P0,W,CM)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION X1(ND,NV),W(ND),P0(NP),CM(ND,NP)
DIMENSION FO(21),ZO(21),YO(21),XO(21), PP(21)
DIMENSION F(21),X(21),Y(21),Z(21)
DIMENSION AN(21), BN(21), CN(21)
NCYC = NCYC + 1
DELTA = 1.0D-05
N=21 !no atoms
ISW=0
SYM=2
C NX = 0
CCC-----MASSES----------DMO = 2.004245
DMC = 1.0033544
DMD = 1.006277
MASSH = 1.007825
FMC = 13.0033544
FMD = 2.014102
FMO = 15.994915
C**********ASSIGN MASSES TO STRUCTURE***************
DO 17, I=1,7
FO(I)=12.000000
17 F(I)=12.000000
DO 18, I=8,11
FO(I) = 15.994915
18 F(I) = 15.994915
DO 19, I=12,21
FO(I)=1.007825
19 F(I)=1.007825
C----------------------------------------C*********USE PARAMATERS TO OBTAIN GEOMETRY********
C
DO 21, I=1,3
173
C
21
PP(I)= 0.0
CONTINUE
DO 50, I=1,3
PP(I)=P0(I)
50
CONTINUE
CALL GSUB(NP,PP,X,Y,Z)
DO 20, L=1,N
XO(L)=X(L)
YO(L)=Y(L)
ZO(L)=Z(L)
20
CONTINUE
C**********CYCLE THROUGH DATA SETS****************************
DO 100, NQ=1,13,3
DO 60, L=1,N !CYCLE THRU DATA SET
F(L)=FO(L)
60
CONTINUE
IF(NQ.EQ.4) F(12)=FMD
IF(NQ.EQ.7) F(14)=FMD
IF(NQ.EQ.10) F(12)=FMD
IF(NQ.EQ.10) F(14)=FMD
C
IF(NQ.EQ.16) F(9)=FMO + DMO
C
IF(NQ.EQ.19) F(10)=FMO + DMO
ISW=1
IF(NCYC.EQ.9)ISW=1
CALL ROTCONST(N,SYM,F,X,Y,Z,A,B,C,ASYMK,ISW)
ISW=0
W(NQ)=A
W(NQ+1)=B
W(NQ+2)=C
DO 40, K=1,10
PP(K)=P0(K)+DELTA !MOVE ATOMS
CALL GSUB(NP,PP,X,Y,Z)
PP(K)=P0(K)
62
CONTINUE
IF(NQ.EQ.4) F(12)=FMD
IF(NQ.EQ.7) F(14)=FMD
IF(NQ.EQ.10) F(12)=FMD
IF(NQ.EQ.10) F(14)=FMD
C
IF(NQ.EQ.16) F(9)=FMO + DMO
C
IF(NQ.EQ.19) F(10)=FMO + DMO
CALL ROTCONST(N,SYM,F,X,Y,Z,AN(K),BN(K),CN(K),ASYMK,ISW)
40
CONTINUE
DO 70, L=1,N
X(L)=XO(L)
Y(L)=YO(L)
Z(L)=ZO(L)
174
70
CONTINUE
DO 30, K=1,10
CM(NQ,K)=(AN(K)-A)/DELTA
CM(NQ+1,K)=(BN(K)-B)/DELTA
CM(NQ+2,K)=(CN(K)-C)/DELTA
30
CONTINUE
100 CONTINUE
RETURN
END
SUBROUTINE GSUB(NP,PP,X,Y,Z)
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION X(21),Y(21),Z(21),PP(21)
DO 2, I1=1,21
2 Z(I1) = 0.0
C
Z(1)=PP(1)
C#########################################
XCM = PP(1) - 4.57
YCM = PP(2) - 0.07792
PHI = -0.1047
C
PHI = 0.000
C
THT = 0.05
C
GAM = PP(3)
C
EPP = 0.0
C
RH = 0.99
C
RHH= RH
Cnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
X(1) = 0.477797
Y(1) = 1.468200
Z(1) = 0.100057
X(2) = 0.799835
Y(2) = -1.411894
Z(2) = 0.257327
X(3) = 1.867282
Y(3) = 0.877927
Z(3) = 0.124422
X(4) = -0.631010
Y(4) = 0.695567
Z(4) = 0.036638
X(5) = 1.900146
Y(5) = -0.560958
Z(5) = -0.394258
X(6) = -0.547667
Y(6) = -0.777189
Z(6) = 0.030727
X(8) = -1.590489
175
Y(8) = -1.424860
Z(8) = -0.031032
X(9) = -1.878412
Y(9) = 1.209461
Z(9) = -0.102649
X(14) = -2.468724
Y(14) = 0.438582
Z(14) = -0.094158
X(15) = 0.358277
Y(15) = 2.549623
Z(15) = 0.075462
X(16) = 0.967381
Y(16) = -1.423781
Z(16) = 1.344453
X(17) = 0.776653
Y(17) = -2.449404
Z(17) = -0.088033
X(18) = 2.575221
Y(18) = 1.498641
Z(18) = -0.436158
X(19) = 2.200818
Y(19) = 0.897604
Z(19) = 1.173445
X(20) = 1.725406
Y(20) = -0.552873
Z(20) = -1.477181
X(21) = 2.882578
Y(21) = -1.012511
Z(21) = -0.220758
X(7) = (-0.408196*DCOS(PHI) + 0.084999*DSIN(PHI)) + XCM !FA
Y(7) = (-0.408196*DSIN(PHI) + 0.084999*DCOS(PHI)) + YCM
Z(7) = 0.000579
X(10) = (0.121604*DCOS(PHI) - 1.132562*DSIN(PHI)) + XCM !FA
Y(10) = (0.121604*DSIN(PHI) - 1.132562*DCOS(PHI)) + YCM
Z(10) = -0.001207
X(11) = (0.210238*DCOS(PHI) + 1.131568*DSIN(PHI)) + XCM !FA
Y(11) = (0.210238*DSIN(PHI) + 1.131568*DCOS(PHI)) + YCM
Z(11) = -0.000458
X(12) = (-1.503153*DCOS(PHI) + 0.032243*DSIN(PHI)) + XCM !FA
Y(12) = (-1.503153*DSIN(PHI) + 0.032243*DCOS(PHI)) + YCM
Z(12) = 0.005667
X(13) = (1.096936*DCOS(PHI) - 1.028534*DSIN(PHI)) + XCM !FA
Y(13) = (1.096936*DSIN(PHI) - 1.028534*DCOS(PHI)) + YCM
Z(13) = 0.013845
C--------------------------------RETURN
176
END
--------------------------------------------------------------------------------------------------------------------OUTPUTFILE
DATE = 4- 23- 2014
cdo-str1
2 12 1 18
0.0001
0.0001
2415.0439
543.6907
451.6663
2414.7543
530.9216
442.8253
2399.6875
542.9527
450.6175
2399.4147
530.2502
441.8415
20140423
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
GIVE: 1 - TO ENTER SD(Y), 1 - TO SUPP. STAT. OF PARAMS.
1 - TO SUPP. STAT.(Y), 1 - TO SUPP. DER., 1 - TO SUPP. CORR. MAT.
IV, NOVP, NOVC, NOCOUT, NOCORR
0 0 1 0 0
CYCLE NUMBER 1
P0
P1
P1 - P0
0.10000000000D-03 0.22277235720D-01 0.22177235720D-01
0.10000000000D-03 -0.28893702439D+01 -0.28894702439D+01
CYCLE NUMBER 2
P0
P1
P1 - P0
0.22277235720D-01 0.13991872691D+00 0.11764149119D+00
-0.28893702439D+01 -0.12972614552D+01 0.15921087887D+01
CYCLE NUMBER 3
P0
P1
P1 - P0
0.13991872691D+00 0.22073231777D+00 0.80813590851D-01
-0.12972614552D+01 -0.14209497996D+01 -0.12368834439D+00
CYCLE NUMBER 4
P0
P1
P1 - P0
0.22073231777D+00 0.22103865096D+00 0.30633319485D-03
-0.14209497996D+01 -0.14163467322D+01 0.46030674394D-02
CYCLE NUMBER 5
177
P0
P1
0.22103865096D+00
-0.14163467322D+01
CYCLE NUMBER 6
P0
P1
0.22103930990D+00
-0.14163449076D+01
CYCLE NUMBER 7
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 8
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 9
P0
P1
0.22103930968D+00
-0.14163449075D+01
CYCLE NUMBER 10
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 11
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 12
P0
P1
0.22103930968D+00
-0.14163449075D+01
CYCLE NUMBER 13
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 14
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 15
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 16
P0
P1
0.22103930967D+00
P1 - P0
0.22103930990D+00
-0.14163449076D+01
0.65893427087D-06
0.18245971096D-05
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.22248786630D-09
0.12962591226D-09
P1 - P0
0.22103930967D+00
-0.14163449075D+01
0.62811837494D-12
-0.16524500184D-11
P1 - P0
0.22103930968D+00
-0.14163449075D+01
0.22115728228D-11
-0.38187188125D-11
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.26123210449D-11
0.57538844699D-11
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.10168986130D-11
0.54184644716D-11
P1 - P0
0.22103930968D+00
-0.14163449075D+01
0.58627913436D-11
-0.15900929920D-10
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.35611516124D-11
0.11209571425D-10
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.17245218625D-11
-0.13708987052D-11
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.10537043629D-11
0.24392305692D-11
P1 - P0
0.22103930967D+00
-0.14163449075D+01
-0.32226538526D-12
0.45376270377D-11
P1 - P0
0.22103930967D+00
-0.48938464829D-12
178
-0.14163449075D+01
CYCLE NUMBER 17
P0
P1
0.22103930967D+00
-0.14163449075D+01
CYCLE NUMBER 18
P0
P1
0.22103930967D+00
-0.14163449075D+01
-0.14163449075D+01
0.88048758532D-12
P1 - P0
0.22103930967D+00
-0.14163449075D+01
0.33435425643D-11
-0.11010899233D-10
P1 - P0
0.22103930967D+00
-0.14163449074D+01
-0.31614138923D-11
0.13488119104D-10
*** FINAL VALUES OF THE PARAMETERS AND STANDARD DEVIATIONS ***
I
1
2
YMEAS
2415.0439
543.6907
451.6663
2414.7543
530.9216
442.8253
2399.6875
542.9527
450.6175
2399.4147
530.2502
441.8415
P0(I)-PARAMETER
0.22103930967D+00
-0.14163449074D+01
YCALC
2417.1848
543.7113
450.8779
2413.7931
531.4466
442.2975
2400.6990
543.2486
449.9907
2397.5249
531.0291
441.4666
S.D.(PARAM)
0.31247004707D-02
0.56979328075D-02
DEV.
-2.1410
-0.0206
0.7884
0.9613
-0.5250
0.5278
-1.0115
-0.2959
0.6267
1.8897
-0.7789
0.3749
SUM OF SQUARED RESIDUES = 0.12505837899D+02
STANDARD DEVIATION FOR FIT = 0.11182950370D+01
THE VALUES IN THE FINAL MATRIX OF DERIVATIVES:
0
-0.261409D+02 0.827665D+02
0.167262D+03 0.528275D+02
0.114112D+03 0.392077D+02
-0.267200D+02 0.856229D+02
0.163463D+03 0.510108D+02
0.112324D+03 0.382072D+02
-0.295460D+02 0.940284D+02
179
0.166761D+03
0.113383D+03
-0.300366D+02
0.162999D+03
0.111635D+03
0.524003D+02
0.392573D+02
0.967196D+02
0.506198D+02
0.382642D+02
0
VARIANCE-COVARIANCE MATRIX OF PARAMETERS
0
0.780736D-05 -0.660423D-05
-0.660423D-05 0.259610D-04
0
CORRELATION COEFFICIENT MATRIX OF PARAMETERS
0
0.100000D+01 -0.463884D+00
-0.463884D+00 0.100000D+01
0
TYPE 1 IF THERE ARE MORE DATA TO BE FITTED:
0
--------------------------------------------------------------------------------------------------------------------The following is the input file needed of the molecular structure Cartesian
coordinates (or Z-matrix) of the molecular species of interest (shown are the
coordinates of ferrocenecarboxylic acid) to start an optimization computation in the
Gaussian program. The first two lines in the file are where the memory and number of
processors are specified. The third line is where the keywords of the computation are
specified (for example if it is an optimization, a scan of the potential energy surface by
rotating a bond or whether or not vibrational frequencies are calculated, then these
keywords are opt, scan, and freq – the keywords can be found on the Gaussian website
and are described in great detail). This line is also where the computational method and
basis set of the computation are chosen, in this case CCSD is the method with a basis
set of cc-pVDZ (these methods and basis set keywords are also given in the Gaussian
documentation with great detail). The fifth line is the title line. The following line, the 0
180
and 1 represent the charge and multiplicity of the molecular species of interest, in this
case the charge is zero and the molecule is in a singlet state with zero unpaired
electrons. Following these specifications, the molecular coordinates or Z-matrix of the
molecular are written.
--------------------------------------------------------------------------------------------------------------------%Mem=2GB
%NProcs=8
#P CCSD/cc-pVDZ opt NoSymm output=pickett
FcA nosym using cc-pVDZ/cc-pVDZ
01
C
C
C
H
C
H
C
H
H
C
H
C
C
H
C
H
C
H
H
Fe
C
O
O
H
-1.385554 0.551631 0.024903
-0.769884 1.161139 1.162709
-0.806665 1.127488 -1.151147
-0.994594 0.923197 2.187902
0.171356 2.106648 0.689604
-1.058517 0.867689 -2.164422
0.148857 2.086393 -0.735071
0.810775 2.720587 1.301502
0.767365 2.683207 -1.384470
0.981888 -1.857185 -0.002714
0.199479 -2.597696 -0.005868
1.566841 -1.268926 1.152034
1.579821 -1.268048 -1.150498
1.310051 -1.492225 2.173825
2.528429 -0.314663 0.717658
1.337173 -1.491411 -2.175785
2.536433 -0.313847 -0.704690
3.129623 0.312978 1.353924
3.145012 0.314152 -1.333496
0.648003 0.194722 -0.003301
-2.410875 -0.493067 0.101862
-2.870971 -0.950745 1.121884
-2.825705 -0.910106 -1.124867
-3.502503 -1.584009 -0.968624
---------------------------------------------------------------------------------------------------------------------
181
The following is the PBS script file needed to submit Gaussian jobs into the
queueing system that will run jobs on the high performance computing system at the
University of Arizona. The file shown is to specifically run jobs on the ocelote system.
This script file where the input file is specified and the memory and time needed to run
the computation are designated. Lines preceding with ### are commented out of the file
and will not be read by the system. Comments have been left throughout the script file
to indicate what each line represents.
--------------------------------------------------------------------------------------------------------------------#!/bin/csh
### Refer to docs.hpc.arizona.edu website for more detailed system documentation
### Set the job name
#PBS -N FcCOOH
### Request an email be sent when computation job begins and ends
#PBS -m bea
### Specify the email address to use for these notifications
#PBS -M pejlovas@email.arizona.edu
### Specify the PI (principle investigator) of the research group for the computation
#PBS -W group_list=kukolich
### Set the queue for the computation on windfall or standard systems (adjust with ###
### and # to comment out and read which system to run)
#PBS -q standard
###PBS -q windfall
### Set the number of cores/cpus and memory that will be used for the job
### When specifying memory, request less than 2GB memory per ncpus for standard
### node. Some memory needs to be reserved for the Linux system processes
#PBS -l select=1:ncpus=28:mem=168gb:pcmem=6gb
#PBS -l place=pack:shared
#PBS -l pvmem=23gb
#PBS -l walltime=100:00:00
#PBS -l cput=1000:00:00
### Specify "wall clock time" required for the computation, hhh:mm:ss
### Specify total cpu time required for the computation, hhh:mm:ss (total cputime =
###walltime * ncpus)
### Load required modules/libraries if needed and se "module avail" command to list all
###available modules
module load gaussian/g09-D.01
module list
### Your jobname.o file will show the path to the execution directory
182
echo $GAUSS_EXEDIR
### set your scratch space file location
set SCR = /rsgrps/kukolich/
setenv GAUSS_ARCDIR $SCR
setenv GAUSS_SCRDIR $SCR
### Be sure the following path is your execution directory
### The last item on the next line is the input file for the Gaussian computation
###(FcCOOH.inp)
date
time $GAUSS_EXEDIR/g09 FcCOOH.inp
date
echo exit status = $?
--------------------------------------------------------------------------------------------------------------------The following are the various files needed to run Dr. Herb Pickett’s SPCAT and
SPFIT programs. The first file listed is the .int file and is needed to run SPCAT. This is
the file where the calculated dipole moment components (from the Gaussian
optimization) and value of the rotational partition function (shown as 1527.9640) are
specified, depending on what temperature is chosen (right most number in the second
lines, shown as 1.0 K). The rotational partition function is calculated using the rotational
constants designated in the .var file and can be adjusted once the program is initiated
and ran for the first time. The partition function and dipole moment component values
are needed in order for the intensities of each of the transitions to be predicted. The
second file is called the .var file and this file is also needed to run SPCAT. This is the
file where the optimized values of the rotational constants are specified, as well as
additional information such as the nuclear spin of quadrupolar nuclei in the molecule.
The input of these rotational constants can be provided by the Gaussian optimization if
the keyword “output=Pickett” is designated on the keyword line, described previously.
The errors listed for each of the constants specified in the .var file are typically set very
small (10-30) as these are calculated values and are shown as zero if the input is taken
183
from the Gaussian optimization. After performing the microwave fits of the measured
spectra (using SPFIT) the .var file is updated with the new updated values for the
constants, as well as errors, so the transitions can be predicted more accurately if they
are assigned correctly.
The third file listed is needed for SPFIT and this is the .par file. This has the
same formatting as the .var file, but now the number of parameters to be fit needs to be
specified as well as how many rotational transitions are to be used in the fit. The errors
for each of the specified constants are typically set very large (1030) when the parameter
is set to be fit from the data. The remaining file needed to run SPFIT is the .lin file. This
file is where the quantum number assignments for each rotational energy level are
assigned. There are three .lin files shown for reference: the first shows the formatting of
the quantum numbers when there are two quadrupolar nuclei, the second file is when
there is only one quadrupolar nucleus, and the last is when there are no quadrupolar
nuclei present. The formatting for all of these files is essential to run the programs
correctly.
--------------------------------------------------------------------------------------------------------------------BNnaphthalene
0112 00001 1527.9640 0 10 -8.0 -8.0 11.0 1.0
2 1.6 /b dipole
--------------------------------------------------------------------------------------------------------------------BNnaphthalene 11B
Fri JThu Nov 12 09:36:56 2015
8 73 50 0 0.0000E+000 1.0000E+016 1.0000E+000 1.0000000000
'a' 34 1 0 15 0 2 1 1
0 1
10000 3.042712752532214E+003 4.82859920E-004 / A /
20000 1.202706572964331E+003 3.86452065E-004 / B /
30000 8.622201276096232E+002 4.04395535E-004 / C /
110010000 -3.922079665937628E+000 8.38534541E-003 / (17 B-11
110040000 -9.068881718801244E-001 2.76689206E-003 / (17 B-11
184
220010000 2.578113459404607E+000 6.85316189E-003 / (18 N-14
220040000 -1.184730921187949E-001 1.93472338E-003 / (18 N-14
200 -5.647561432827691E-005 1.07823178E-005 / -DJ
--------------------------------------------------------------------------------------------------------------------BNnaphthalene 11B
Fri JThu Nov 12 09:36:56 2015
8 73 50 0 0.0000E+000 1.0000E+016 1.0000E+000 1.0000000000
'a' 34 1 0 15 0 2 1 1
0 1
10000 3.042712752532214E+003 1.00000000E+037 / A /
20000 1.202706572964331E+003 1.00000000E+037 / B /
30000 8.622201276096232E+002 1.00000000E+037 / C /
110010000 -3.922079665937628E+000 1.00000000E+037 / (17 B-11
110040000 -9.068881718801244E-001 1.00000000E+037 / (17 B-11
220010000 2.578113459404607E+000 1.00000000E+037 / (18 N-14
220040000 -1.184730921187949E-001 1.00000000E+037 / (18 N-14
200 -5.647561432827691E-005 4.33624533E+036 / -DJ
--------------------------------------------------------------------------------------------------------------------Line file from BN-naphthalene (2 quadrupolar nuclei)
1 1 0 3 2 1 0 1 1 1
2179.7240
0.005
1 1 0 1 1 1 0 1 3 2
2179.7813
0.005
1 1 0 1 1 1 0 1 2 1
2179.9329
0.005
1 1 0 3 2 1 0 1 3 3
2179.9571
0.005
1 1 0 2 3 1 0 1 1 2
2180.2341
0.005
1 1 0 3 4 1 0 1 3 4
2180.3198
0.005
1 1 0 3 4 1 0 1 2 3
2180.8807
0.005
1 1 0 2 3 1 0 1 3 2
2181.1696
0.005
2 0 2 2 1 1 1 1 3 2
2246.0699
0.005
2 0 2 3 4 1 1 1 3 4
2246.1470
0.005
2 0 2 2 3 1 1 1 2 3
2246.6648
0.005
2 0 2 2 2 1 1 1 1 1
2246.7358
0.005
2 0 2 4 4 1 1 1 3 4
2247.3151
0.005
2 0 2 1 2 1 1 1 1 1
2247.4661
0.005
2 1 1 4 3 2 0 2 1 2
2562.9129
0.005
2 1 1 2 3 2 0 2 1 2
2563.1467
0.005
2 1 1 2 3 2 0 2 4 4
2563.3627
0.005
2 1 1 3 4 2 0 2 4 5
2563.9003
0.005
2 1 1 3 2 2 0 2 2 3
2563.9272
0.005
2 1 1 3 2 2 0 2 2 1
2563.9517
0.005
2 1 1 1 2 2 0 2 2 3
2563.9928
0.005
2 1 1 3 3 2 0 2 4 3
2564.0394
0.005
2 1 1 3 4 2 0 2 2 3
2564.1451
0.005
2 1 1 2 3 2 0 2 3 2
2564.7382
0.005
2 1 1 3 3 2 0 2 3 3
2564.8827
0.005
185
1
1
1
1
1
3
3
3
3
3
3
5
5
5
3
3
6
6
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
5
5
5
1
1
1
1
1
0
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
3
3
3
3
3
1
1
1
1
1
3
3
3
3
3
3
3
3
3
1
1
4
4
0
0
0
0
0
0
0
0
2
2
2
2
2
3
3
3
3
4
4
5
5
5
5
3
3
3
3
3
3
2
2
3
3
3
4
5
4
2
3
4
6
6
2
4
5
8
1
4
1
1
4
1
4
2
2
5
4
2
2
3
2
4
4
4
3
5
6
4
7
6
4
6
7
5
3
2
3
4
2
2
5
4
4
2
2
4
7
5
2
4
4
9
2
4
1
1
3
1
4
1
3
4
4
3
3
3
2
5
3
4
2
5
5
4
6
7
4
6
6
4
0
0
0
0
0
2
2
2
2
2
2
5
5
5
3
3
6
6
2
2
2
2
2
2
2
2
1
1
1
3
3
2
2
4
4
3
3
4
4
4
4
5
5
5
5
5
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
2
2
2
2
2
4
4
4
2
2
5
5
1
1
1
1
1
1
1
1
1
1
1
3
3
2
2
4
4
3
3
4
4
4
4
4
4
4
4
4
2
2
2
2
2
2
3
4
3
1
3
4
7
7
2
4
5
8
2
3
1
3
3
1
4
2
3
3
3
2
2
2
1
3
3
5
2
4
5
3
5
7
4
6
5
5
2
3
2
3
3
1
4
3
3
1
2
4
8
6
3
3
4
9
1
3
2
2
3
1
3
1
2
4
4
2
3
3
2
4
2
4
1
4
4
4
5
6
3
6
6
4
3904.6352
3904.6973
3904.9352
3905.0188
3905.4868
4484.1528
4484.4399
4484.5142
4484.5903
4484.6792
4484.7446
5011.6021
5011.7275
5011.7778
5248.8096
5249.3145
5302.4146
5302.4692
5562.0176
5562.1392
5562.2998
5562.3691
5562.4224
5562.4722
5562.7515
5563.0088
5629.4268
5629.5298
5629.6841
7076.6250
7076.8428
7201.3242
7201.3672
7800.8184
7800.9487
8675.9053
8676.3770
10128.1406
10128.2158
10128.6934
10128.7666
10397.6445
10397.6816
10397.8994
10397.9766
10398.0127
186
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
5 3 3 5 5 5 2 4 5 6
5 3 3 6 7 5 2 4 6 7
10398.0547
10398.0947
0.005
0.005
--------------------------------------------------------------------------------------------------------------------Line file from maleimide (one quadrupolar nucleus)
1 1 0 1 1 0 1 1
5059.7046
0.005
1 1 0 1 1 0 1 2
5060.1914
0.005
1 1 0 2 1 0 1 1
5060.7686
0.005
1 1 0 1 1 0 1 0
5060.9170
0.005
1 1 0 2 1 0 1 2
5061.2568
0.005
1 1 0 0 1 0 1 1
5062.3672
0.005
2 1 1 2 2 0 2 2
5725.5610
0.005
2 1 1 2 2 0 2 3
5726.1904
0.005
2 1 1 3 2 0 2 3
5726.8076
0.005
2 1 1 1 2 0 2 1
5727.4976
0.005
3 1 2 3 3 0 3 3
6827.3027
0.005
3 1 2 4 3 0 3 3
6827.7744
0.005
3 1 2 2 3 0 3 3
6827.9375
0.005
3 1 2 3 3 0 3 4
6828.1113
0.005
3 1 2 3 3 0 3 2
6828.4028
0.005
3 1 2 4 3 0 3 4
6828.5864
0.005
3 1 2 2 3 0 3 2
6829.0381
0.005
3 0 3 2 2 1 2 2
8214.5664
0.005
3 0 3 4 2 1 2 3
8215.9912
0.005
3 0 3 2 2 1 2 1
8216.3369
0.005
3 0 3 3 2 1 2 3
8216.7988
0.005
4 1 3 4 4 0 4 4
8466.0400
0.005
4 1 3 5 4 0 4 5
8467.4316
0.005
4 1 3 3 4 0 4 3
8467.7949
0.005
1 1 1 0 0 0 0 1
8568.6826
0.005
1 1 1 2 0 0 0 1
8569.5527
0.005
1 1 1 1 0 0 0 1
8570.1250
0.005
5 2 3 5 5 1 4 5
11862.7266
0.005
5 2 3 6 5 1 4 6
11862.7617
0.005
4 0 4 4 3 1 3 3
12726.9668
0.005
4 0 4 5 3 1 3 4
12727.2832
0.005
4 0 4 3 3 1 3 2
12727.4932
0.005
4 2 2 3 4 1 3 3
12191.2578
0.005
4 2 2 5 4 1 3 5
12191.2920
0.005
--------------------------------------------------------------------------------------------------------------------Line file from cyclopropanecarboxylic acid (no quadrupolar nuc)
1 0 1 0 0 0
5204.936
0.005
2 1 2 1 1 1
10035.056
0.005
187
2
2
1
1
2
3
2
4
0
1
1
1
1
1
0
1
2
1
1
0
1
2
2
3
1
1
0
1
2
3
1
4
0
1
0
0
0
0
1
0
1
0
0
1
2
3
1
4
10388.154
10784.638
9867.375
5037.232
5433.717
6068.218
5725.706
6984.654
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
--------------------------------------------------------------------------------------------------------------------
188
9. WORKS CITED
1. Legon, A.C. Pulsed-Nozzle, Fourier-Transform Microwave Spectroscopy of Weakly
Bound Dimers. Ann. Rev. Phys. Chem. 34 (1983) 275-300.
2. P. R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, 2nd ed., NRC
Research Press, Ottawa, 2006. 3. R. E. Bumgarner and S. G. Kukolich. Microwave Spectra and Structure of HI-HF
Complexes. J. Chem Phys. 86 (1987) 1083.
4. B. S. Tackett, C. Karunatilaka, A. M. Daly, and S. G. Kukolich. Microwave Spectra
and Gas-Phase Structural Parameters of Bis(η5-cyclopentadienyl)tungsten Dihydride.
Organometallics 26/8 (2007) 2070-2076. http://dx.doi.org/10.1021/om061027f
5. Daly, A. M. Gas Phase Structures and Molecular Constants of Dimers and Molecules
Determined Using Microwave Spectroscopy. Ph.D. Dissertation. The University of
Arizona 2010.
6. Gordy, W.; Cook, R. L. Microwave Molecular Spectra; Chemical Applications of
Spectroscopy IX; John Wiley & Son Inc.: New York, 1968 and 1970.
7. H.W. Kroto. Molecular Rotation Spectra. Dover Publications, Inc. New York, 1992.
8. H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371.
http://spec.jpl.nasa.gov/ftp/pub/calpgm/spinv.html
9. R. A. Fiesner, R. B. Murphy, M. D. Beachy, M. N. Ringualda, W. T. Pllard, B.D.
Dunietz and Y. Cao J.Phys. Chem. A. 18 (1999) 1913.
10. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman,
J.R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.A., et al. Gaussian 09,
Revision A.02, Gaussian, Inc., Wallingford CT, 2009.
189
11. Kimura, T.; Hattori, Y.; Momochi, H.; Nakaya, N.; Satoh, T. Synlett. 24 (2013) 483486.
12. Duncombe, W.G.; Rising, T.J. Biochem. J. 109 (1968) 449-455.
13. Aratani, T. Pure & Appl. Chem. 57/12 (1985) 1839-1844.
14. Hirao, T.; Harano, Y.; Yamana, Y.; Hamada, Y. Bull. Chem. Soc. Jpn. 59 (1986)
1341-1347.
15. H.M. Badawi. A.A. Al-Saadi. M.A.A. Al-Khaldi. S.A. Al-Abbad. Z.H.A. Al-Sunaidi.
Spectrochimica Acta Part A. 71 (2008) 1540–1546.
16. de Boer, J. S. A. M.; Stam, C.H. Recueil des Travaux Chimiques des Pays-Bas.
111/9 (1992) 407-410.
17. Maillols, J.; Tabacik, V.; Sportouch, S. Journal of Molecular Structure. 32 (1976)
173-190.
18. Marstokk, K. M.; Møllendal, H.; Samdal, S. Acta Chemica Scandinavica. 45 (1991)
37-45.
19. A.M. Pejlovas, K. Li, S.G. Kukolich. Microwave measurements of
cyclopropanecarboxylic acid and –OD isotopologue. Journal of Molecular Spectroscopy.
313 (2015) 1-3.
20. A.M. Pejlovas, W.Lin, and S.G. Kukolich. Microwave Spectrum for a Second Higher
Energy Conformer of Cyclopropanecarboxylic Acid and Determination of the Gas Phase
Structure of the Ground State. J. Phys. Chem. A. 119/39 (2015) 10016-10021.
21. Z. Kisiel , <http://www.ifpan.edu.pl/~kisiel/struct/struct.htm#kra>
22. Antoniotti, S.; Duñach, E. Studies on the Catalytic Oxidation of Epoxides to αdiketones by Bi(0)/O2 in DMSO. J. of Mol. Catal. A: Chem. 208 (2004) 135-145.
190
23. Antoniotti, S.; Duñach, E. Novel and Catalytic Oxidation of Internal Epoxides to αdiketones. Chem. Commun. 24 (2001) 2566-2567.
24. Simpkins, C.M.; Hunt, D.A. The Michael Addition of 1,2-cyclohexanedione to βnitrostyrenes (I): The Synthesis of 3-aryl-5,6-dihydrobenzofuran-7(4H)-ones.
Tetrahedron Lett. 54 (2013) 3371-3373.
25. Wolt, J., Flavoring Foodstuffs with a Mixture Containing 1,2-Cyclohexanedione. US
Patent 3,875,307. April 1, 1975.
26. Montazeri, N.; Oliveira, A.C.M.; Himelbloom, B.H.; Leigh, M.B.; Crapo, C.A.
Chemical Characterization of Commercial Liquid Smoke Products. Food Sci. and Nutr.
1 (2013) 102-115.
27. Patthy, L.; Smith, E.L. Reversible Modification of Arginine Residues: Application to
Sequence Studies by Restriction of Tryptic Hydrolysis to Lysie Residues. J. of Biol.
Chem. 250 (1975) 557-564.
28. Heiland, I.; Wittmann-Liebold, B. Amino Acid Sequence of the Ribosomal Protein
L21 of Escherichia Coli. Biochemistry.I 18 (1979) 4605-4612.
29. De Borger, L.; Anteunis, M.; Lammens, H.; Verzele, M. 1,2-Cyclohexanedione. Bull.
Soc. Chim. 73 (1964) 73-80.
30. Shen, Q.; Traetteberg, M.; Samdal, S. The Molecular Structure of Gaseous 1,2Cyclohexanedione. J. of Mol. Struct. 923 (2009) 94-97.
31. Samanta, A.K.; Pandey, P.; Bandyopadhyay, B.; Chakraborty, T. Keto-enol
Tautomers of 1,2-Cyclohexanedione in Solid, Liquid, Vapour and a Cold Inert Gas
Matrix: Infrared Spectroscopy and Quantum Chemistry Calculation. J. of Mol. Struct.
963 (2010) 234–239.
191
32. Bumgarner, R.E. Microwave Spectroscopy of Weakly Bound Complexes and High
Resolution Infrared Studies of the ν6 and ν8 Bands of Formic Acid. Ph.D. Dissertation.
Department of Chemistry, University of Arizona. (1988) 221-227.
33. Frogner, M.; Johnson, R. D.; Hedberg, L.; Hedberg, K., J. Phys. Chem A. 117
(2013) 11101-11106
34. Blanco, Susana; Lesarri, Alberto; Lopez, Juan C.; Alonso, Jose L. J. Am. Chem.
Soc. 126 (2004) 11675.
35. S.G. Kukolich, M. Sun, A.M. Daly, W. Luo, L.N. Zakharov, S. Liu. Identification and
characterization of 1,2-BN cyclohexene using microwave spectroscopy. Chem. Phys.
Lett. 639 (2015) 88-92. http://dx.doi.org/10.1016/j.cplett.2015.09.009
36. W. Gordy, and R.L. Cook, Microwave Molecular Spectra, Wiley-Interscience, New
York, 1984. 37. Lauer, M.H. Drekener, R.L. Correia, C.R. and Gehlen, M.H. Photochem. Photobiol.
Sci. 13 (2014) 859
38. Benkova, B. Journal of Chromatography B. 870/1 (2008) 103-108.
39. Thale, P.B. Borase, P.N. and Shankarling, G.S. RSC Advances, 4/103 (2014)
59454-59461.
40. Osby, J. O. Martin, M. G. and Ganem, B. Tetrahedron Lett. 25 (1984) 2093–2096.
41. Mathur, P. Joshi, R.K. Rai, D.K. Jhaa. B. and Mobinb, S.M. Dalton Trans. 41 (2012)
5045.
42. Lin, K.F. Lin, J.S. Cheng, C.H. Polymer. 37/21 (1996) 4729–4737.
43. Matheus, M. Sirqueira, A.S. and Soares, B.G. Polymer Testing. 29/7 (2010) 840848.
192
44. Birkinshaw, J. H. Kalyanpur, M.G. and Stickings, C.E. Biochem. J. 86 (1963) 237–
243.
45. Roberts, M.J. Bentley, M.J. and Harris, J. M. Advanced drug delivery reviews. 64
(2012) 116-127.
46. Moore, E. and Pickelman, D. Industrial & Engineering Chemistry Product Research
and Development. 25/4 (1986) 603-609.
47. Rinkes, I.J. Rec. Trav. Chim. 48 (1929) 961.
48. Taherpour, A. Abramian, A. Kardanyazd, H. Asian Journal of Chemistry 18/3 (2006)
2401-2403. 49. Baltá-Calleja, F. J. Ramos, J. G. and Barrales-Rienda, J. M. Kolloid-Zeitschrift und
Zeitschrift für Polymere. 250/5 (1972) 474-481.
50. Harsányi, L. Vajda, E. and Hargittai, I. Journal of molecular structure. 129/3 (1985)
315-320.
51. T. Oka. Journal of Molecular Structure. 352/353 (1995) 225-233.
52. M.A. Motaleb, L.Y. Abdel-Ghaney, H.M. Abdel-Bary, H.A. Shamsel-Din. J.
Radioanal. Nucl. Chem. 307/1 (2015) 363-372. DOI:10.1007/s10967-015-4140-3.
53. Kishida, K. Aoyama, A. Hasimoto, Y. Miyachi, H. Chem. Pharm. Bull. 58. 11 (2010)
1525-1528.
54. T. W. Green, P. G. M. Wuts, “Protective Groups in Organic Synthesis,” WileyInterscience, New York. (1999) 564-566, 740-743.
55. L.J. Winters and W.E. McEwen. Tetrahedron. 19 (1963) 49-56.
56. W. A. Noyes and P. K. Porter. Org. Syn. 2 (1922) 75.
193
57. M.A.V. Ribeiro da Silva. Claudia P.F. Santos. M.J.S. Monte. C.A.D. Sousa. J.
Therm. Anal. Cal. 83 (2006) 533-539.
58. Matzat, E. Acta. Cryst. B28 (1972) 415-418.
59. Binev, I.G. Stamboliyska, B.A. Binev, Y.I. Velcheva, E.A. Tsenov, J.A. Journal of
Molecular Structure. 513 (1999) 231-243.
60. Choudhury M. Zakaria. John N. Low. Christopher Glidewell. Acta. Cryst. C58 (2002)
o9-o10
61. A. Staubitz, A.P.M. Robertson, I. Manners. Chem. Rev. 110 (2010) 4079.
62. Z. Huang, T. Autrey. Energy Environ. Sci. 5 (2012) 9257.
63. (a) M. Bowden, S.T. Autrey, I. Brown, M. Ryan, Curr. Appl. Phys. 8 (2008) 498;
(b) W.J. Shaw, J.C. Linehan, N.K. Szymczak, D.J. Heldebrant, C. Yonker,
D.M.Camaioni, R.T. Baker, T. Autrey, Angew. Chem. Int. Ed. Engl. 47 (2008) 7493.
64. (a) T.M. Douglas, A.B. Chaplin, A.S. Weller. J. Am. Chem. Soc. 130 (2008) 14432;
(b) M.C. Denney, V. Pons, T.J. Hebden, D.M. Heinekey, K.I. Goldberg. J. Am. Chem.
Soc. 128 (2006) 12048; (c) N. Blaquiere, S. Diallo-Garcia, S.I. Gorelsky, D.A. Black, K.
Fagnou. J. Am. Chem. Soc. 130 (2008) 14034; (d) M.E. Sloan, A. Staubitz, T.J. Clark,
C.A. Russell, G.C. Lloyd-Jones, I. Manners. J. Am. Chem. Soc. 132 (2010) 3831;
(e) D.W. Himmelberger, C.W. Yoon, M.E. Bluhm, P.J. Carroll, L.G. Sneddon. J. Am.
Chem. Soc. 131 (2009) 14101.
65. G. Chen, L.N. Zakharov, M.E. Bowden, A.J. Karkamkar, S.M. Whittemore,
E.B.Garner, T.C. Mikulas, D.A. Dixon, T. Autrey, S.-Y. Liu. J. Am. Chem. Soc. 137
(2015) 134.
194
66. P.G. Campbell, L.N. Zakharov, D.J. Grant, D.A. Dixon, S.-Y. Liu. J. Am. Chem.
Soc.132 (2010) 3289.
67. (a) W. Luo, P.G. Campbell, L.N. Zakharov, S.-Y. Liu. J. Am. Chem. Soc. 133 (2011)
19326; (b) W. Luo, D. Neiner, A. Karkamkar, K. Parab, E.B. Garner, D.A. Dixon, D.
Matson,T. Autrey, S.-Y. Liu. Dalton Trans. 42 (2013) 611.
68. P.G. Campbell, J.S.A. Ishibashi, L.N. Zakharov, S.-Y. Liu. Aust. J. Chem. 67 (2013)
521.
69. Forrest, S. R.; Thompson, M. E. Chem. Rev. 107 (2007) 923.
70. (a) Bencini, A.; Lippolis, V. Coord. Chem. Rev. 256 (2012) 149; (b) Formica, M.;
Fusi, V.; Giorgi, L.; Micheloni, M. Coord. Chem. Rev. 256 (2012) 170; (c) Wade, C. R.;
Brooms grove, A. E. J.; Aldridge, S.; Gabbaï, F. P. Chem. Rev. 110 (2010) 3958.
71. (a) Hatakeyama, T.; Hashimoto, S.; Seki, S.; Nakamura, M. J. Am. Chem. Soc. 133
(2011) 18614; (b) Hatakeyama, T.; Hashimoto, S.; Oba, T.; Nakamura, M. J. Am. Chem.
Soc. 134 (2012) 19600; (c) Wang, X.; Lin, H.; Lei, T.; Yang, D.; Zhuang, F.; Wang, J.;
Yuan, S.; Pei, J. Angew. Chem., Int. Ed. 52 (2013) 3117; (d) Lepeltier, M.; Lukoyanova,
O.; Jacobson, A.; Jeeva, S.; Perepichka, D. F. Chem. Commun. 46 (2010) 7007; (e)
Zhou, Z.; Wakamiya, A.; Kushida, T.; Yamaguchi, S. J. Am. Chem. Soc. 134 (2012)
4529.
72. (a) Neue, B.; Araneda, J. F.; Piers, W. E.; Parvez, M. Angew. Chem., Int. Ed. 52
(2013) 9966; (b) Jaska, C. A.; Emslie, D. J. H.; Bosdet, M. J. D.; Piers, W. E.; Sorensen,
T. S.; Parvez, M. J. Am. Chem. Soc. 128 (2006) 10885; (c) Bosdet, M. J. D.; Piers, W.
E.; Sorensen, T. S.; Parvez, M. Angew. Chem., Int. Ed. 46 (2007) 4940; (d) Wisniewski,
S. R.; Guenther, C. L.; Argintaru, O. A.; Molander, G. A. J. Org. Chem. 79 (2014) 365.
195
73. F. Sun; L. Lv; M. Huang; Z. Zhou; X. Fang. Organic Letters. 16 (2014) 5024-5027.
74. W. Luo, L.N. Zakharov, S.-Y. Liu. J. Am. Chem. Soc. 133 (2011) 13006.
75. S.G. Kukolich; M. Sun; A.M. Daly; W. Luo; L.N. Zakharov; Shih-Yuan Liu. Chemical
Physics Letters. 639 (2015) 88-92.
76. A.M. Daly, C. Tanjaroon, A.J.V. Marwitz, S.-Y. Liu, S.G. Kukolich. J. Am. Chem.
Soc. 132/15 (2010) 5501.
77. Abbey, E. R.; Zakharov, L. N.; Liu, S.-Y. J. Am. Chem. Soc. 130 (2008) 7250–7252.
78. Novick, S.E. Journal of Molecular Spectroscopy. 267 (2011) 13-18.
79. Kang, L.; Sunahori, F.; Minei, A. J.; Clouthier, D. J.; Novick, S. E. J. Chem. Phys.
130 (2009) 124317.
80. C. Tanjaroon, A. Daly, A.J.V. Marwitz, S.-Y. Liu, S. Kukolich. J. Chem. Phys. 131/22
(2009) 224312/1.
81. A. Konovalov, H. Mollendal, J.-C. Guillemin. J. Phys. Chem. A. 113/29 (2009) 8337.
82. D. Fujiang, P.W. Fowler, A.C. Legon. J. Chem. Soc. Chem. Commun. 1 (1995) 113.
83. Legon, A. C.; Warner, H. E. J. Chem. Soc., Chem. Commun. (1991) 1397–1399.
84. L.R. Thorne, R.D. Suenram, F.J. Lovas. J. Chem. Phys. 78/1 (1983) 167.
85. M. Sugie, H. Takeo, C. Matsumura. Chem. Phys. Lett. 64 (1979) 573.
86. Vormann, K.; Dreizler, H.; Doose, J.; Guarnieri, A. Z. Naturforsch. A. 46 (1991) 770–
776.
87. F.J. Lovas, D.R. Johnson. J. Chem. Phys. 59 (1973) 2347.
88. T.S. Briggs, W.D. Gwinn, W.L. Jolly, L.R. Thorne. J. Am. Chem. Soc. 100 (1978)
7762.
196
89. Reeve, S. W.; Burns, W. A.; Lovas, F. J.; Suenram, R. D.; Leopold, K. R. J. Phys.
Chem. 97 (1993) 10630–10637.
90. X. Fang; H. Yang; J.W. Kampf; M.M.B. Holl, A.J. Ashe III. Organometallics. 25
(2006) 513-518.
91. Rohr, A. D.; Kampf, J. W.; Ashe, A. J. III. Organometallics. 33 (2014) 1318. 92. S.G. Kukolich and L.C. Sarkozy. Rev. Sci. Instrum. 82 (2011) 094103;
http://dx.doi.org/10.1063/1.3627489
93. Bohn, R. K.; Hillig, K. W., II; Kuczkowski, R. L. J. Phys. Chem. 93 (1989) 3456–
3459.
94. P. O. Löwdin. Adv. Quantum Chem. 2 (1965) 213.
95. J. Catalan, M. Kasha, J. Phys. Chem. A. 104 (2000) 10812.
96. Daly, A. M.; Bunker, P. R.; Kukolich, S. G. J. Chem. Phys. 132/20 (2010) 201101/1.
97. Daly, A. M.; Bunker, P. R.; Kukolich, S. G. J. Chem. Phys. 133/7 (2010) 079903/1.
98. Daly, A. M.; Douglass, K. O.; Sarkozy, L. C.; Neill, J. L.; Muckle, M. T.; Zaleski, D.
P.; Pate, B. H.; Kukolich, S. G. J. Chem. Phys. 135 (2011) 154304/1−154304/12.
99. Tayler, M. C. D.; Ouyang, B.; Howard, B. J. J. Chem. Phys. 134 (2011)
054316/1−054316/9.
100. Pejlovas, A.M. Barfield, Michael. Kukolich, Stephen G. Chemical Physics Letters.
613 (2014) 86-89.
101. Birer, O.; Havenith, M. Annu. Rev. Phys. Chem. 60 (2009) 263−275.
102. Rowe, W. F.; Duerst, R. W.; Wilson, E. B. J. Am. Chem. Soc. 98 (1976)
4021−4023.
197
103. Baughcum, S. L.; Duerst, R. W.; Rowe, W. F.; Smith, Z.; Wilson, E. B. J. Am.
Chem. Soc. 103 (1981) 6296−6303.
104. Baughcum, S. L.; Smith, Z.; Wilson, E. B.; Duerst, R. W. J. Am. Chem. Soc. 106
(1984) 2260−2265.
105. Turner, P.; Baughcum, S. L.; Coy, S. L.; Smith, Z. J. Am. Chem. Soc. 106 (1984)
2265−2267.
106. K. Tanaka, H. Honjo, T. Tanaka, H. Kohguchi, Y. Ohshima, and Y. Endo. J. Chem.
Phys. 110 (1999) 1969.
107. Keske, J. C.; Lin, W.; Pringle, W. C.; Novick, S. E.; Blake, T. A.; Plusquellic, D. F.
J. Chem. Phys. 124 (2006) 074309.
108. R.W. Davis, A.G. Robiette, M.C.L. Gerry, E. Bjarnov, G. Winnewisser. J. Mol.
Spec. 81 (1980) 93.
109. Kukolich, S. G.; Mitchell, E. G.; Carey, S. J.; Sun, M.; and Sargus, B. A. J. Phys.
Chem. A. 117/39 (2013) 9525–9530.
110. A.M. Pejlovas, M. Barfield, S.G. Kukolich. Journal of Physical Chemistry A. 119
(2015) 1464-1468.
111. Z. Kisiel , < http://www.ifpan.edu.pl/~kisiel/struct/struct.htm#pmifst>
112. A.M. Pejlovas, O. Oncer, L. Kang, and S.G. Kukolich. Journal of Molecular
Spectroscopy. 319 (2016) 26-29.
113. A.K. Chandra. Introductory Quantum Chemistry. 4th Ed. Tata McGraw-Hill
Publishing Company Limited. (1994).
114. A. E. Bracamonte and P. H. Vaccaro. J. Chem. Phys. 120 (2003) 4638.
115. L. A. Burns, D. Murdock, and P. H. Vaccaro. J. Chem. Phys. 124 (2006) 204307.
198
116. D. Murdock, L. A. Burns, and P. H. Vaccaro. J. Chem. Phys. 127 (2007) 081101.
117. L. A. Burns, D. Murdock, and P. H. Vaccaro. J. Chem. Phys. 130 (2009) 144304.
118. D. Murdock, L. A. Burns, and P. H. Vaccaro. Phys. Chem. Chem. Phys. 12
(2010) 8285.
119. R. L. Redington, and T. E. Redington. J. Mol. Spectrosc. 78 (1979) 229.
120. R. L. Redington, and T. E. Redington. J. Chem. Phys. 122 (2005) 124304.
121. R. Rossetti, and L. E. Brus. J. Chem. Phys. 73 (1980) 1546.
122. Y. Tomioka, M. Ito, and N. Mikami. J. Phys. Chem. 87 (1983) 4401.
123. R. L. Redington. J. Chem. Phys. 113 (2000) 2319.
124. R. L. Redington, and R. L. Sams. J. Phys. Chem. A. 106 (2002) 7494.
125. R. L. Redington, T. E. Redington, and R. L. Sams. J. Phys. Chem. A. 110 (2006)
9633.
126. R. L. Redington, T. E. Redington, and R. L. Sams. J. Phys. Chem. A. 112 (2008)
1480.
127. H. Sekiya, T. Nakajima, H. Ujita, T. Tsuji, S. Ito, Y. Nishimura. Chem. Phys. Lett.
215 (1993) 499.
128. W. Lin, W. C. Pringle, S. E. Novick, T. A. Blake. J. Phys. Chem. A. 113 (2009)
13076.
129. J. C. Keske, and D. F. Plusquellic, International Symposium of Molecular
Spectroscopy, TD10, Columbus, OH. (2003).
130. G. G. Brown, B. C. Dian, K. O. Douglass, S. M. Geyer, S. T. Shipman, and B. H.
Pate. Rev. Sci. Instrum. 79 (2008) 053103. https://doi.org/10.1063/1.2919120
199
131. G. G. Brown, B. C. Dian, K. O. Douglass, S. M. Geyer, and B. H. Pate. J. Mol.
Spectrosc. 238 (2006) 200. https://doi.org/10.1016/j.jms.2006.05.003
132. K. Prozument, Y. V. Suleimanov, B. Buesser, J. M. Oldham, W. H. Green, A. G.
Suits, and R. W. Field. J. Phys. Chem. Lett. 5 (2014) 3641.
https://doi.org/10.1021/jz501758p
133. C. Abeysekera, B. Joalland, N. Ariyasingha, L. N. Zack, I. R. Sims, R. W. Field,
and A. G. Suits. J. Phys. Chem. Lett. 6 (2015) 1599.
https://doi.org/10.1021/acs.jpclett.5b00519 200
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